document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=833391>Question 833391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cn someone pls help me with this question? tks!\r<BR>\n" );
document.write( "\n" );
document.write( "Is the product of HCF n LCM of any 3 numbers always equal t the product of the 3 numbers? If yes, show 3 pairs as example.<BR>\n" );
document.write( "          If no, show a counter-example.    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #502637 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=502637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> No. Not for 3 numbers<BR>\n" );
document.write( "If you had just 2 numbers, each number would be the product of the greatest/highest common factor times the non-common factors found only in that number. The least common multiple would include all the factor in the greatest/highest common factor, and all the non-common factors. The product <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=HCF%2ALCM ALIGN=MIDDLE  ALT=\"HCF%2ALCM\"   DISABLED_style= \"max-width:90%; height:auto;\" > would include the common factors twice, and the non-common factors once. So would the product of the two numbers. Therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=HCF%2ALCM ALIGN=MIDDLE  ALT=\"HCF%2ALCM\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be equal to the product of the two numbers.<BR>\n" );
document.write( " <BR>\n" );
document.write( "With 3 numbers, the situation is different.<BR>\n" );
document.write( "Factors common to two of the numbers, but not common to all three would be included twice in the product of the three numbers, but only once in the LCM, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LCM%2AHCF ALIGN=MIDDLE  ALT=\"LCM%2AHCF\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Factors from the HCF would be included 3.<BR>\n" );
document.write( "The highest common factor of 10, 12, and 24 is 2.<BR>\n" );
document.write( "The least common multiple is 120.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A12%2A24=2880 ALIGN=MIDDLE  ALT=\"10%2A12%2A24=2880\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=green%282%29%2A5 ALIGN=MIDDLE  ALT=\"10=green%282%29%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=green%282%29%2Ared%286%29 ALIGN=MIDDLE  ALT=\"12=green%282%29%2Ared%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=green%282%29%2Ared%286%29%2A2 ALIGN=MIDDLE  ALT=\"24=green%282%29%2Ared%286%29%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=HCF=green%282%29 ALIGN=MIDDLE  ALT=\"HCF=green%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LCM=green%282%29%2A5%2Ared%286%29%2A2=120 ALIGN=MIDDLE  ALT=\"LCM=green%282%29%2A5%2Ared%286%29%2A2=120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LCM%2AHCF=%28green%282%29%2A5%2Ared%286%29%2A2%29%2A%28green%282%29%29 ALIGN=MIDDLE  ALT=\"LCM%2AHCF=%28green%282%29%2A5%2Ared%286%29%2A2%29%2A%28green%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%282%29 ALIGN=MIDDLE  ALT=\"green%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is included twice.<BR>\n" );
document.write( "The factor common to only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%286%29 ALIGN=MIDDLE  ALT=\"red%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and is included just once.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A12%2A24=%28green%282%29%2A5%29%2A%28green%282%29%2Ared%286%29%29%2A%28green%282%29%2Ared%286%29%2A2%29=green%282%29%2A5%2Agreen%282%29%2Ared%286%29%2Agreen%282%29%2Ared%286%29%2A2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%282%29 ALIGN=MIDDLE  ALT=\"green%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is included 3 times, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%286%29 ALIGN=MIDDLE  ALT=\"red%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is included twice. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );