MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C95D3C.2A4E1130" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM

This presentation contains content that your browser may not be able to = show properly. This presentation was optimized for more recent versions of Micro= soft Internet Explorer.

If you would like to proceed anyway, click here.

 ------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/master25.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
Click to edit Master title style
Click to edit Master text styles
Second level
Third level
Fourth level
Fifth level
‹date/time›
‹footer›
‹#›
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/master25.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD3wAAAAUANgAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAEAAAALQEAAAQAAAAnAf//HAAAAPsC1P8A AAAAAACQAQAAAAAAQAAiQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQA AAAuARgABAAAAAIBAQAFAAAACQIAAAACNgAAADIKMACYAB8AAABUaGUgTGVhc3QgQ29tbW9uIE11 bHRpcGxlIChMQ00pABsAGAAZAAwAGQAZABgAFgANAAwAIAAYACYAJgAYABgADAAmABgACgAMAAoA GQAKABgADAAQABgAIAAlAA8ABAAAAC4BAAAcAAAA+wIQAAcAAAAAALwCAAAAAAECAiJTeXN0ZW0A AAAAAAAYAAAAmLETAAEAAADkBAAAAAAAAAQAAAAtAQQABAAAAPABAwADAAAAAAA= ------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0004.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
The Least Common Multiple (LCM)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0038.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
We say m is a multiple= of x if m can be divided= by x.
The Least Common Multiple (LCM)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0039.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2
The Least Common Multiple (LCM)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0040.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
The Least Common Multiple (LCM)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0041.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
The Least Common Multiple (LCM)
xy2 is a multiple of x,
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0042.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
The Least Common Multiple (LCM)
xy2 is a multiple of x, xy2 is also a multiple of= y or xy.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0043.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
The Least Common Multiple (LCM)
A <= /span>common multi= ple of two or more quantities= is a multiple of all the given quantities.
xy2 is a multiple of x, xy2 is also a multiple of= y or xy.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0044.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
The Least Common Multiple (LCM)
A common multiple of two or more quantities= is a multiple of all the given quantities.
For example, 24 is a common multiple of 4 and 6,
xy2 is a multiple of x, xy2 is also a multiple of= y or xy.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0045.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
The Least Common Multiple (LCM)
A common multiple of two or more quantities= is a multiple of all the given quantities.
For example, 24 is a common multiple of 4 and 6,
xy2 is a multiple of x, xy2 is also a multiple of= y or xy.
xy2 is a common multiple of x and y. <= /span>
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0046.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
The= least common multiple (LCM) of two or more numbers is the smallest common multiple of= all the given numbers.
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
The Least Common Multiple (LCM)
A common multiple of two or more quantities= is a multiple of all the given quantities.
For example, 24 is a common multiple of 4 and 6,
xy2 is a multiple of x, xy2 is also a multiple of= y or xy.
xy2 is a common multiple of x and y. <= /span>
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0047.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
The= least common multiple (LCM) of two or more numbers is the smallest common multiple of= all the given numbers.
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
For example, 12 is the LCM of 4 and 6.
The Least Common Multiple (LCM)
A common multiple of two or more quantities= is a multiple of all the given quantities.
For example, 24 is a common multiple of 4 and 6,
xy2 is a multiple of x, xy2 is also a multiple of= y or xy.
xy2 is a common multiple of x and y. <= /span>
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0048.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
The= least common multiple (LCM) of two or more numbers is the smallest common multiple of= all the given numbers.
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
For example, 12 is the LCM of 4 and 6.
The Least Common Multiple (LCM)
A common multiple of two or more quantities= is a multiple of all the given quantities.
For example, 24 is a common multiple of 4 and 6,
We give two methods for finding the LCM.
xy2 is a multiple of x, xy2 is also a multiple of= y or xy.
xy2 is a common multiple of x and y. <= /span>
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0049.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
The= least common multiple (LCM) of two or more numbers is the smallest common multiple of= all the given numbers.
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
For example, 12 is the LCM of 4 and 6.
The Least Common Multiple (LCM)
A common multiple of two or more quantities= is a multiple of all the given quantities.
For example, 24 is a common multiple of 4 and 6,
We give two methods for finding the LCM.
I. The searching method
xy2 is a multiple of x, xy2 is also a multiple of= y or xy.
xy2 is a common multiple of x and y. <= /span>
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0050.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
The= least common multiple (LCM) of two or more numbers is the smallest common multiple of= all the given numbers.
We say m is a multiple= of x if m can be divided= by x.
For example, 12 is a multiple of 2 and 12= is also a multiple of 3, 4, 6 or 12 itself. =
For example, 12 is the LCM of 4 and 6.
The Least Common Multiple (LCM)
A common multiple of two or more quantities= is a multiple of all the given quantities.
For example, 24 is a common multiple of 4 and 6,
We give two methods for finding the LCM.
I. The searching method
II. The construction method
xy2 is a multiple of x, xy2 is also a multiple of= y or xy.
xy2 is a common multiple of x and y. <= /span>
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0036.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Search= ing Method
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0051.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0052.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 1= 6.
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0053.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24:
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0054.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72,
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0067.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0066.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0055.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Construction Method: 
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0068.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,<= /span>
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0069.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0070.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Example B.&nb= sp; a. Construct the LCM of 18, 24, 20.
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0071.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Example B.  a. Constru= ct the LCM of 18, 24, 20.
Factor each number completely
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0072.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Example B.  a. Constru= ct the LCM of 18, 24, 20.
Factor each number completely
18 =3D 2*32
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0073.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Example B.  a. Constru= ct the LCM of 18, 24, 20.
Factor each number completely
18 =3D 2*32
24 =3D 233
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Example B.  a. Constru= ct the LCM of 18, 24, 20.
Factor each number completely
18 =3D 2*32
24 =3D 233
20 =3D 225
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0075.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Example B.  a. Constru= ct the LCM of 18, 24, 20.
Factor each number completely
18 =3D 2*32
24 =3D 233
20 =3D 225
Take the highest of the each factor,
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0076.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Example B.  a. Constru= ct the LCM of 18, 24, 20.
Factor each number completely
18 =3D 2*32
24 =3D 233
20 =3D 225
Take the highest of the each factor,
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0078.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Example B.  a. Constru= ct the LCM of 18, 24, 20.
Factor each number completely
18 =3D 2*32
24 =3D 233
20 =3D 225
Take the highest of the each factor,
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0077.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Example B.  a. Constru= ct the LCM of 18, 24, 20.
Factor each number completely
18 =3D 2*32
24 =3D 233
20 =3D 225 =
Take the highest of the each factor,
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0079.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
Searching Method &#= 13;
Given a list quantitie= s, list the multiples of the largest quantity one by on= e until we find the LCM. 
Example A.  Find the LCM of 18, 24, 16.
List the multiples of 24: 24, 48, 72, 96, 120, 144, …
We find = the LCM of {18, 24, 16} is 144.  =
Methods of Findi= ng LCM
Example B.  a. Constru= ct the LCM of 18, 24, 20.
Factor each number completely
18 =3D 2*32
24 =3D 233
20 =3D 225 =
Take the highest of the each factor,
so the LCM is 2325 =3D 360.
Construction Method:  Given two or more quantities, = ;
I.  factor each quantity completely,&= #13;
II. multiply the highest power of each factor appeared in the factorization to get the LCM.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0034.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2y3z, x= yz4, x<= span lang=3DEN-US style=3D'mso-hansi-font-family:Arial;font-size:89%;color:#003= 300; position:relative;top:-.45em;mso-text-raise:30%;mso-fareast-language:ZH-CN= '>3zw
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0080.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0082.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
Factor e= ach quantities.
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0083.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
Factor e= ach quantities.
x= 2 – 3x + 2  =3D (x – 2)(x – 1)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0084.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
Factor e= ach quantities.
x= 2 – 3x + 2  =3D (x – 2)(x – 1) 
x= 2 + x – 2 =3D (x + 2)(x – 1) 
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0085.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
Factor e= ach quantities.
x= 2 – 3x + 2  =3D (x – 2)(x – 1) 
x= 2 + x – 2 =3D (x + 2)(x – 1)  
Take the highest power of each factor, we get the
LCM =3D = (x – 2)(x – 1)(x +2)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0086.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
d.  Construct the LCM of x4 – 4x2, x2 – 4x +4
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
Factor e= ach quantities.
x= 2 – 3x + 2  =3D (x – 2)(x – 1) 
x= 2 + x – 2 =3D (x + 2)(x – 1)  
Take the highest power of each factor, we get the
LCM =3D = (x – 2)(x – 1)(x +2)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0087.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
d.  Construct the LCM of x4 – 4x2, x2 – 4x +4
Factor e= ach quantities.
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
Factor e= ach quantities.
x= 2 – 3x + 2  =3D (x – 2)(x – 1) 
x= 2 + x – 2 =3D (x + 2)(x – 1)  
Take the highest power of each factor, we get the
LCM =3D = (x – 2)(x – 1)(x +2)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0088.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
d.  Construct the LCM of x4 – 4x2, x2 – 4x +4
Factor e= ach quantities.
x= 4 – 4x2 =3D x2(x2 – 4)
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
Factor e= ach quantities.
x= 2 – 3x + 2  =3D (x – 2)(x – 1) 
x= 2 + x – 2 =3D (x + 2)(x – 1)  
Take the highest power of each factor, we get the
LCM =3D = (x – 2)(x – 1)(x +2)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0089.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
d.  Construct the LCM of x4 – 4x2, x2 – 4x +4
Factor e= ach quantities.
x= 4 – 4x2 =3D x2(x2 – 4) =3D x2(x + 2)(x – 2)=
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
Factor e= ach quantities.
x= 2 – 3x + 2  =3D (x – 2)(x – 1) 
x= 2 + x – 2 =3D (x + 2)(x – 1)  
Take the highest power of each factor, we get the
LCM =3D = (x – 2)(x – 1)(x +2)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0090.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
d.  Construct the LCM of x4 – 4x2, x2 – 4x +4
Factor e= ach quantities.
x= 4 – 4x2 =3D x2(x2 – 4) =3D x2(x + 2)(x – 2) 
x= 2 – 4x + 4 =3D (x – 2)2 
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
Factor e= ach quantities.
x= 2 – 3x + 2  =3D (x – 2)(x – 1) 
x= 2 + x – 2 =3D (x + 2)(x – 1)  
Take the highest power of each factor, we get the
LCM =3D = (x – 2)(x – 1)(x +2)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0091.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
b. Construct the LCM of x2yz, x3yz, x3zw
All quantities are factored, take the highest power of each = factor, so the LCM =3D x3y3zw.
Methods of Findi= ng LCM
d.  Construct the LCM of x4 – 4x2, x2 – 4x +4
Factor e= ach quantities.
x= 4 – 4x2 =3D x2(x2 – 4) =3D x2(x + 2)(x – 2) 
x= 2 – 4x + 4 =3D (x – 2)2  
Take the highest power of each factor, we get the
LCM =3D = x2(x ̵= 1; 2)2(x +2)
c.  Construct the LCM of x2 – 3x + 2, x2 – x – 2
Factor e= ach quantities.
x= 2 – 3x + 2  =3D (x – 2)(x – 1) 
x= 2 + x – 2 =3D (x + 2)(x – 1)  
Take the highest power of each factor, we get the
LCM =3D = (x – 2)(x – 1)(x +2)
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0016.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
The Construction Method takes just enough of ea= ch factor to make the LCM that cove= rs all the quantities on the list.
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0092.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
The Construction Method takes just enough of each factor to make the LCM that covers all the quantities on the list.
The following is an example that illustrates the principle behind this method .
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0094.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
The Construction Method takes just enough of each factor to make the LCM that covers all the quantities on the list.
The following is an example that illustrates the principle behind this method .
Example C. A student wants to take enough courses so she meets the requirement to apply to three different colleges
A, B, and C.  The following is a table of requirements, how many years of each subject does she need?
1 yrs=
4 yrs=
2 yrs=
2 yrs=
C
2 yrs=
3 yrs=
3 yrs=
B
3 yrs=
3 yrs=
2 yrs=
A
Arts<= /div>
English
Math.=
Science
Methods of Findi= ng LCM
------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0094_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh5AGAAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADj AX4AgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4YiBpTmiabqyrbuC59BTNf2Tc/4zvev7gsKecCh 8ehCIJdMVLEJHT6jVGL12ptit78D9xvTgscmMXlsPn/T6q2y3WbDq/J5tG5v4vPLN3/9B7YXKEXI NWjo45dIhci44/h4EylZQ1kZ5oWpt8nZ2fcJGnq0OBp0aZqCmirDKrTqClAaO0mbZWuFiwPrOqsL w8sanDpsWjzq+5ukbHMc6vwJ3ZnMvCK9eY2ZXbktSV2tCh4mDkz+Y56kiW69ztL9+M4Yn/iNPm94 T5gfuP9Xb96PT8A8A+0UnPOP3EE4C+O0Y/dQlbqIZSg6sdgKY4mG/2oSiuN4BiQZkWg0bpxokaQg k7JYqlyDkuLLQy5rmvQIbqYbmxp1YsFZzecVoXR4YgTKjGgjoyldxoyo9A5TmU4NTIV69WFUKEiV bfXUM2u7rr++MjErKuzNp1rFrkOLBC4ptmPd2rMLcITevXz7+v0LOLDgwYQLJ8CrEPHHqnKNNC50 U3FOum8lB7WclPLdyJzV9tQMELNX0WVBJ+58lLQusqtV43r8irFrW7BPzabF+vXtWLUVyUbdFDjV tVaFYzXelnjvW8jrNn9revHzzZ6PRs+5u1d2YdcvTw/9XWH3pNuJlTc2fnR46dVTpi97Hln8Z+9b r8d+P2h93fnJ9//3uh9t80Uz4DQB4lYgNglqcyBvC3LzoDcNavcffBWuNqEwEcKzoTwZmnchf+3J 9KExHdJzIj4lyheigC3ituIzKeozIz8xEviigzn2YliPPv4IZJBCDklkkcvlMuJxSWp14zQ1+vOk QE0quKOGVRIzpTZRErSlQVlCeKWJYSLzpTddInQmQ2VyOKaMbUazpjxpOvSmgcUt6RyelSk3Z0d9 hvSbntSlVic2caJYqJaJcnMoPn+O9CgajdK4qJmVwjMpP5GudKmHdxIqKHihivdpcKOyB6p1pQ53 Kn6t6reqkqmaOiuJsSb3qn+5AnhrnrXKSqt7ve65q4XFYjjsoMH/svork8mK2qyvy0KVKZSdInrs a9UKtCkg16r47GnZujgujOGiOi2u0UJ3rqvrKsussEdC0i1N3+pjZL767stvv/7+60G9O92rKZ8E W1uujp+1613CFDrMHcO6vgttumNty+XB3GpMEMYGCfwTyEN5jCbHH5uMEMkMiVwUympKrB7EIMqM HszGUiwuzh+pTCfNLPpMn832AY0j0XbOuwvLS7kcB89+Mv200YYKLaLO7lrMLtK1QA0o1yM53bXU iorNKNXkWt0w2pmZjaDXJbktCNiQwu0t2RKyrbDaMetdGt4P8z004Nr6baXdbBruqdbNKC0V3YfI /Tbi2ApOG+ScOEruqONuWF435W1jji/hM3ueN9b2cG4v6AWr7g/qA7O+MewdA0x77bbfjnvuuu/O e+++/w78AgUAADs= ------=_NextPart_01C95D3C.2A4E1130 Content-Location: file:///C:/1F764DE5/5TheLeastCommonMultiple_files/slide0095.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM