document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1408>Question 1408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what the freak is the l.c.m AND the g.c.d. of 82, 96 and 112?  i'm too tired to try this anymore!<BR>\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #489 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what the freak is the l.c.m AND the g.c.d. of 82, 96 and 112? i'm too tired to<BR>\n" );
document.write( "try this anymore! Thanks!\r<BR>\n" );
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document.write( "It's asking \"What is the smallest integer that 82,96 and 112 will divide into evenly?\r<BR>\n" );
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document.write( "Prime factor 82:\r<BR>\n" );
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document.write( "82 = 2·41\r<BR>\n" );
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document.write( "Prime factor 96\r<BR>\n" );
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document.write( "96 = 2·48 = 2·2·24 = 2·2·2·12 = 2·2·2·2·6 = 2·2·2·2·2·3\r<BR>\n" );
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document.write( "Prime factor 112\r<BR>\n" );
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document.write( "96 = 2·56 = 2·2·28 = 2·2·2·14 = 2·2·2·2·7\r<BR>\n" );
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document.write( "So we have\r<BR>\n" );
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document.write( "82 = 2·41\r<BR>\n" );
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document.write( "96 = 2·2·2·2·2·3\r<BR>\n" );
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document.write( "112 = 2·2·2·2·7\r<BR>\n" );
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document.write( "82 contains 2 ONE time, 96 contains 2 FIVE times, 112 contains 2 FOUR times.\r<BR>\n" );
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document.write( "The largest of ONE, FIVE and FOUR is FIVE, so the LCM must contain 2 FIVE times.\r<BR>\n" );
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document.write( "82 contains 41 ONE time, 96 contains 41 ZERO times, 112 contains 41 ZERO\r<BR>\n" );
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document.write( "times.  The largest of ONE, ZERO and ZERO is ONE, so the LCM must contain 41\r<BR>\n" );
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document.write( "ONE time.\r<BR>\n" );
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document.write( "96 contains 3 ONE time, 82 contains 3 ZERO times, 112 contains 3 ZERO times. \r<BR>\n" );
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document.write( "The largest of ONE, ZERO and ZERO is ONE, so the LCM must contain 3 ONE time.\r<BR>\n" );
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document.write( "112 contains 7 ONE time, 82 contains 7 ZERO times, 96 contains 7 ONE times. \r<BR>\n" );
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document.write( "The largest of ONE, ZERO and ZERO is ONE, so the LCM must contain 7 ONE time.\r<BR>\n" );
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document.write( "So the LCM is the integer that contains 2 FIVE times, 41 ONE time, 3 ONE time,\r<BR>\n" );
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document.write( "and 7 ONE time is 2·2·2·2·2·41·3·7 = 27552 <BR>\n" );
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document.write( "Edwin\r<BR>\n" );
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