document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62072>Question 62072</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this homework problem.  The least common multiple of 2 numbers is 3780, and the greatest common factor is 18.  Given that one of the numbers is 180, what is the other number?\r<BR>\n" );
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document.write( "I started out by 3780/180= 21.  But 18 is not a factor of 21?  What am I doing wrong?<BR>\n" );
document.write( "Thanks!<BR>\n" );
document.write( "Laura </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42833 by </B><A HREF=/tutors/aboutme.mpl?userid=joyofmath><B>joyofmath(189)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=joyofmath><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=42833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <b>The least common multiple of 2 numbers is 3780, and the greatest common factor is 18.  Given that one of the numbers is 180, what is the other number?</b>\r<BR>\n" );
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document.write( "To solve these GCF and LCM problems, factor the numbers you're working with into primes:\r<BR>\n" );
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document.write( "3780 = 2*2*3*3*3*5*7<BR>\n" );
document.write( "180 = 2*2*3*3*5\r<BR>\n" );
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document.write( "We know that the LCM of the two numbers, call them A and B, = 3780 and that A = 180. The greatest common factor of 180 and B = 18 so B has factors 2*3*3 in common with 180 but no other factors in common with 180. So, B has no more 2's and no 5's. <BR>\n" );
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document.write( "Now, LCM(180,B) = 3780. So, A or B must have each of the factors of 3780. B needs another factor of 3 and a factor of 7 since LCM(A,B) needs for either A or B to have a factor of 2*2, which A has, and a factor of 3*3*3, which B will have with another factor of 3, and a factor of 7, which B will have.\r<BR>\n" );
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document.write( "So, B = 2*3*3*3*7 = 378.<BR>\n" );
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document.write( "Here's a website that calculates GCF and LCM for you that you can use to verify the answer.<BR>\n" );
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document.write( "http://www.venturaes.com/coolstuff/GCF_LCM.html<BR>\n" );
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