document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78172>Question 78172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble with a question from my school text book and I have asked my teacher but I am still confused. The question is list two numbers with a HCF of 12 and a LCM of 180. I have asked my mum and and she doesn't get it. She checked in the awnsers fo me but that didn't help either. So can you please show me step by step workings to solve this problem. Thank you.     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56068 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=56068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x=1st number, y=second number\r<BR>\n" );
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document.write( "Since the LCM is the product of the 2 numbers divided by the GCF we have\r<BR>\n" );
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document.write( "LCM: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180=%28x%2Ay%29%2F12 ALIGN=MIDDLE  ALT=\"180=%28x%2Ay%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So multiply both sides by 12\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay=2160 ALIGN=MIDDLE  ALT=\"x%2Ay=2160\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the product of the 2 numbers is 2160. We know that in order to have a GCF of 12, the lowest number is 12. So lets try x=12\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y=2160 ALIGN=MIDDLE  ALT=\"12y=2160\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=12\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=180 ALIGN=MIDDLE  ALT=\"y=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 12\r<BR>\n" );
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document.write( "So our second number is 180\r<BR>\n" );
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document.write( "Now lets find the GCF and the LCM between these 2 numbers:\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=find_greatest_common_factor.solver>Find Greatest Common Factor</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>First, factorise 180 and 12:<BR>\n" );
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document.write( "  Factors of 180: 2,2,3,3,5<BR>\n" );
document.write( "  Factors of 12: 2,2,3.<BR>\n" );
document.write( "Highlight common factors:<BR>\n" );
document.write( "  180: <FONT COLOR=RED>2</FONT>,<FONT COLOR=RED>2</FONT>,<FONT COLOR=RED>3</FONT>,3,5<BR>\n" );
document.write( "  12: <FONT COLOR=RED>2</FONT>,<FONT COLOR=RED>2</FONT>,<FONT COLOR=RED>3</FONT><BR>\n" );
document.write( "  Common factors: 2,2,3<BR>\n" );
document.write( "The product of these common factors is:2*2*3=12.<BR>\n" );
document.write( "This number, 12, is your greatest common factor:<BR>\n" );
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document.write( "  <U>Greatest Common Factor( 180, 12 ) = 12</U>.<BR>\n" );
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document.write( "Now lets find the LCM\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=least_common_multiple.solver>Compute Least Common Multiple</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>LCM of two numbers can be calculated simply: calculate the product of these numbers and divide them by their greatest common factor (GCF). That's what we are going to do. <BR>\n" );
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document.write( "  Calculate GCF of 180 and 12: <BR>\n" );
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document.write( "  The product of 180 and 12, divided by the GCF 12, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2A12%2F12+=+180 ALIGN=MIDDLE  ALT=\"180%2A12%2F12+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  So, 180 is the least common multiple of 180 and 12.</TD></TR>\n" );
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document.write( "We got lucky on our first try. So it turns out that the two numbers are\r<BR>\n" );
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document.write( "12,180\r<BR>\n" );
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