document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118367>Question 118367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the LCM and GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B10x%5E2%2B25x ALIGN=MIDDLE  ALT=\"x%5E3%2B10x%5E2%2B25x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2B5x%5E3 ALIGN=MIDDLE  ALT=\"x%5E4%2B5x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86487 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86487\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find either the Least Common Multiple (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LCM ALIGN=MIDDLE  ALT=\"LCM\"   DISABLED_style= \"max-width:90%; height:auto;\" >) or Greatest Common Factor (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=GCF ALIGN=MIDDLE  ALT=\"GCF\"   DISABLED_style= \"max-width:90%; height:auto;\" >) of two numbers (or expressions), you always start out the same way: you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=find+ ALIGN=MIDDLE  ALT=\"find+\"   DISABLED_style= \"max-width:90%; height:auto;\" >the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=prime+ ALIGN=MIDDLE  ALT=\"prime+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=factorizations ALIGN=MIDDLE  ALT=\"factorizations\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the two numbers(or expressions).\r<BR>\n" );
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document.write( "so, we will factor it first:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+10x%5E2+%2B+25x ALIGN=MIDDLE  ALT=\"x%5E3+%2B+10x%5E2+%2B+25x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%5E2+%2B+10x+%2B+25%29 ALIGN=MIDDLE  ALT=\"x%28x%5E2+%2B+10x+%2B+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >………notice that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+10x+%2B+25 ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+10x+%2B+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > is square of the sum of two numbers\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x+%2B+5%29%5E2 ALIGN=MIDDLE  ALT=\"x%28x+%2B+5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >………\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x+%2B+5%29%28x+%2B+5%29 ALIGN=MIDDLE  ALT=\"x%28x+%2B+5%29%28x+%2B+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >……… the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=prime ALIGN=MIDDLE  ALT=\"prime\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+factors ALIGN=MIDDLE  ALT=\"+factors\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now factor the other expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B+5x%5E3+ ALIGN=MIDDLE  ALT=\"x%5E4+%2B+5x%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >……..factor out common <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%28x%2B+5%29+ ALIGN=MIDDLE  ALT=\"x%5E3%28x%2B+5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >……..or…..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ax%2Ax%28x%2B+5%29+ ALIGN=MIDDLE  ALT=\"x%2Ax%2Ax%28x%2B+5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >…….. the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=prime ALIGN=MIDDLE  ALT=\"prime\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+factors ALIGN=MIDDLE  ALT=\"+factors\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now write them in order:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E3+%2B+10x%5E2+%2B+25x+=+x%28x+%2B+5%29%28x+%2B+5%29 ALIGN=MIDDLE  ALT=\"+x%5E3+%2B+10x%5E2+%2B+25x+=+x%28x+%2B+5%29%28x+%2B+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >………\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B+5x%5E3+%85%85%85..=+x%2Ax%2Ax%28x%2B+5%29+ ALIGN=MIDDLE  ALT=\"x%5E4+%2B+5x%5E3+%85%85%85..=+x%2Ax%2Ax%28x%2B+5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LCM ALIGN=MIDDLE  ALT=\"LCM\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the smallest expression that both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+10x%5E2+%2B+25x ALIGN=MIDDLE  ALT=\"x%5E3+%2B+10x%5E2+%2B+25x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B+5x%5E3+ ALIGN=MIDDLE  ALT=\"x%5E4+%2B+5x%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > will divide into, or it is the smallest expression that contains both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+10x%5E2+%2B+25x ALIGN=MIDDLE  ALT=\"x%5E3+%2B+10x%5E2+%2B+25x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B+5x%5E3+ ALIGN=MIDDLE  ALT=\"x%5E4+%2B+5x%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (that both expressions fit in to), we will have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LCM+=+x%2Ax%2Ax%28x+%2B+5%29%28x+%2B+5%29+=+x%5E3%28x%5E2+%2B+10x+%2B+25%29 ALIGN=MIDDLE  ALT=\"LCM+=+x%2Ax%2Ax%28x+%2B+5%29%28x+%2B+5%29+=+x%5E3%28x%5E2+%2B+10x+%2B+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >………\r<BR>\n" );
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document.write( "since the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+GCF+ ALIGN=MIDDLE  ALT=\"+GCF+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the biggest expression that will divide into both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+10x%5E2+%2B+25x+ ALIGN=MIDDLE  ALT=\"x%5E3+%2B+10x%5E2+%2B+25x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B+5x%5E3+ ALIGN=MIDDLE  ALT=\"x%5E4+%2B+5x%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >(inother words, it's the expression that contains all the common factors), the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=GCF ALIGN=MIDDLE  ALT=\"GCF\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=product ALIGN=MIDDLE  ALT=\"product\"   DISABLED_style= \"max-width:90%; height:auto;\" > of any and all factors that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+10x%5E2+%2B+25x ALIGN=MIDDLE  ALT=\"x%5E3+%2B+10x%5E2+%2B+25x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B+5x%5E3+ ALIGN=MIDDLE  ALT=\"x%5E4+%2B+5x%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > share. It will be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=GCF+=+x%28x%2B5%29+=+x%5E2+%2B+5x ALIGN=MIDDLE  ALT=\"GCF+=+x%28x%2B5%29+=+x%5E2+%2B+5x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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