document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825146>Question 825146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you work out the lcm of two numbers<BR>\n" );
document.write( "what is the lcm of 32 and 14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497076 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497076\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> LCM, Lowest Common Multiple.\r<BR>\n" );
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document.write( "Just make several of the first whole number multiples of each number and look for the first multiple or product which occurs for both of the given numbers.\r<BR>\n" );
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document.write( "___________14______________32<BR>\n" );
document.write( "2__________28______________64<BR>\n" );
document.write( "3__________42______________96<BR>\n" );
document.write( "4__________56______________128<BR>\n" );
document.write( "5__________70______________160<BR>\n" );
document.write( "6__________84______________192<BR>\n" );
document.write( "7__________98______________224<BR>\n" );
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document.write( "Still not done...\r<BR>\n" );
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document.write( "Want better way?\r<BR>\n" );
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document.write( "Factor each given starter number into its prime factorization.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14=2%2A7 ALIGN=MIDDLE  ALT=\"14=2%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32=4%2A8=2%5E2%2A2%5E3=2%5E5 ALIGN=MIDDLE  ALT=\"32=4%2A8=2%5E2%2A2%5E3=2%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The LCM you want is the number which has the highest count of each of the involved prime factors of each given number.  The 7 occurs 1 time; the 2 occurs 5 times.  The lowest common multiple for 14 and 32 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%287%2A2%5E5=highlight%28224%29%29 ALIGN=MIDDLE  ALT=\"highlight%287%2A2%5E5=highlight%28224%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Obviously found was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A32=224 ALIGN=MIDDLE  ALT=\"7%2A32=224\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but you can examine this factorization to see how 14 is used as one of the factors to get 224 as product:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2A2%5E4=14%2A16=224 ALIGN=MIDDLE  ALT=\"14%2A2%5E4=14%2A16=224\"   DISABLED_style= \"max-width:90%; height:auto;\" >;  you see already how one-by-one separate multiplications can consume so much time. </SPAN>\n" );
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