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<title>Exercise:  Find the LCM </title>
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<div class=3DSection1>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'>Exercise:</b>=
<span
style=3D'mso-spacerun:yes'>&nbsp; </span>Find the LCM </p>

<p class=3DMsoNormal>1.<span style=3D'mso-spacerun:yes'>&nbsp; </span>a.{6,=
 8}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;
</span>b. {6, 9}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;
</span>c. {3, 4}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;
</span>d. {4, 10}<span style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'><o:p>&nbsp;=
</o:p></span></p>

<p class=3DMsoNormal>2.<span style=3D'mso-spacerun:yes'>&nbsp; </span>a.{5,=
 6,
8}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>b. {4, 6, 9}<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;
</span>c. {3, 4, 5}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>d. {4, 6, 10}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;
</span></p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'><o:p>&nbsp;=
</o:p></span></p>

<p class=3DMsoNormal>3.<span style=3D'mso-spacerun:yes'>&nbsp; </span>a.{6,=
 8,
9}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>b. {6, 9, 10}<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;
</span>c. {4, 9, 10}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>d. {6, 8, 10}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;
</span></p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'><o:p>&nbsp;=
</o:p></span></p>

<p class=3DMsoNormal>4.<span style=3D'mso-spacerun:yes'>&nbsp; </span>a.{4,=
 8,
15}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>b. {8, 9, 12}<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>c. {6, 9, 15}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'><o:p>&nbsp;=
</o:p></span></p>

<p class=3DMsoNormal>5.<span style=3D'mso-spacerun:yes'>&nbsp; </span>a.{6,=
 8,
15}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>b. {8, 9, 15}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>c. {6, 9, 16}<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </s=
pan></p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'><o:p>&nbsp;=
</o:p></span></p>

<p class=3DMsoNormal>6.<span style=3D'mso-spacerun:yes'>&nbsp; </span>a.{8,=
 12,
15}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>b. { 9, 12, 15}<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>c. { 9, 12, 16}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'><o:p>&nbsp;=
</o:p></span></p>

<p class=3DMsoNormal>7.<span style=3D'mso-spacerun:yes'>&nbsp; </span>a.{8,=
 12,
18}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>b. {8, 12, 20}<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>c. { 12, 15, 16} </p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'><o:p>&nbsp;=
</o:p></span></p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'>8</span>.<s=
pan
style=3D'mso-spacerun:yes'>&nbsp; </span>a.{8, 12, 15, 18}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;</span>b.
{8, 12, 16, 20}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'><o:p>&nbsp;=
</o:p></span></p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'>9</span>.<s=
pan
style=3D'mso-spacerun:yes'>&nbsp; </span>a.{8, 15, 18, 20}<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>b. {9, 16, 20, 24}<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </sp=
an></p>

<p class=3DMsoNormal><span style=3D'mso-fareast-language:ZH-CN'><o:p>&nbsp;=
</o:p></span></p>

<p class=3DMsoNormal>1<span style=3D'mso-fareast-language:ZH-CN'>0</span>.<=
span
style=3D'mso-spacerun:yes'>&nbsp; </span>A high school student wants to take
enough classes so she can apply to three different unversities A, B and C.<=
span
style=3D'mso-spacerun:yes'>&nbsp; </span>Uof A requires 3 years of English,=
 4
years of mathematics and 2 years of arts.<span style=3D'mso-spacerun:yes'>&=
nbsp;
</span>U of B requires<span style=3D'mso-spacerun:yes'>&nbsp; </span>4 year=
s of
English, 4 years of mathematics and 1 years of arts.<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>U of C requires 3 years of
English, 3 years of mathematics and 3 years of arts.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>How many years of each subjects sh=
ould
she take so that she is qualified for all thre schools?<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></p>

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