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------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/master12.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD3wAAAAUANgAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAEAAAALQEAAAQAAAAnAf//HAAAAPsC1P8A AAAAAACQAQAAAAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQA AAAuARgABAAAAAIBAQAFAAAACQIAAAACNgAAADIKMACYAB8AAABUaGUgTGVhc3QgQ29tbW9uIE11 bHRpcGxlIChMQ00pABsAGAAZAAwAGQAZABgAFgANAAwAIAAYACYAJgAYABgADAAmABgACgAMAAoA GQAKABgADAAQABgAIAAlAA8ABAAAAC4BAAAcAAAA+wIQAAcAAAAAALwCAAAAAAECAiJTeXN0ZW0A AAAAAAAYAAAALJ4TAAEAAADkBAAAAAAAAAQAAAAtAQQABAAAAPABAwADAAAAAAA= ------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0035.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Least Common Multiple LCM
The Least Common Multiple (LCM)
------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0036.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0037.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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.
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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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 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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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)
xy2 is a multiple of x, xy2 is also a multiple of= y or xy.
------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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)
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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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)
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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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 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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0044.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0045.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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. =
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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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,
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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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.
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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0049.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0050.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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. 
Example A.  Find the LCM of 18, 24, 1= 6.
Methods of Findi= ng LCM
------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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, 16.
List the multiples of 24:
Methods of Findi= ng LCM
------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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: 24, 48, 72,
Methods of Findi= ng LCM
------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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, 96, 120, 144, …
Methods of Findi= ng LCM
------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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
------=_NextPart_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0056.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0057.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0058.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0059.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0060.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0061.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0062.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0063.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0064.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_files/slide0065.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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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
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_01C970E3.1E7A52F0 Content-Location: file:///C:/2D664A33/5LCDandMoreOperationsofRationalExpressions_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, …
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.
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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.
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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
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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
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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
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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.
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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)
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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) 
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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Addition and Subtraction of Rational Expressions
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Addition and Subtraction of Rational Expressions
Only fractions with th= e same denominator may be added or subtracted directly.
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Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
=3D
A&plu= smn;B<= /div>
D
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Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;