document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102079>Question 1102079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The LCM of two numbers is between 10 and 20.The two numbers is differ  by 3.What are they? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716826 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=716826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I'm not sure if there is a practical algebraic method for solving this problem that could be applied to more difficult similar problems....<br><BR>\n" );
document.write( "We could find the answer by logical analysis...<br><BR>\n" );
document.write( "(1) Two numbers that differ by 3 and have an LCM between 10 and 20 must both be single digit numbers.<BR>\n" );
document.write( "(2) If two single digit numbers have an LCM between 10 and 20 (i.e., greater than either of the two numbers), then the larger number can't be a multiple of the first; if it were, then the LCM would be the larger of the two numbers.<br><BR>\n" );
document.write( "So the two single digit numbers have to be different multiples of some single digit number.  The only two such numbers are 2*3=6 and 3*3=9.<br><br><BR>\n" );
document.write( "But by far the easiest way to solve this problem is to look at all the pairs of single digit numbers that differ by 3 and find the pair for which the LCM is between 10 and 20:<BR>\n" );
document.write( "1 and 4: LCM 4<BR>\n" );
document.write( "2 and 5: LCM 10  (not \"between 10 and 20\")<BR>\n" );
document.write( "3 and 6: LCM 6<BR>\n" );
document.write( "4 and 7: LCM 28<BR>\n" );
document.write( "5 and 8: LCM 40<BR>\n" );
document.write( "6 and 9: LCM 18 </SPAN>\n" );
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