document.write( "Question 464643: Find the LCM of 21a^2b^6, 3a^4b^8, 14a^5b^8\r
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Algebra.Com's Answer #318303 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor's solution is wrong.\r\n" );
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document.write( "Prime factor them all:\r\n" );
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document.write( "21a²b⁶ = 3·7·a·a·b·b·b·b·b·b\r\n" );
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document.write( "3a4b⁸ = 3·a·a·a·a·b·b·b·b·b·b·b·b\r\n" );
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document.write( "14a⁵b⁸ = 2·7·a·a·a·a·a·b·b·b·b·b·b·b·b\r\n" );
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document.write( " Line those up like this so that only like factors\r\n" );
document.write( "are lined up vertically. Then draw a line underneath:\r\n" );
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document.write( "  3·7·a·a      ·b·b·b·b·b·b\r\n" );
document.write( "  3  ·a·a·a·a  ·b·b·b·b·b·b·b·b\r\n" );
document.write( "2  ·7·a·a·a·a·a·b·b·b·b·b·b·b·b\r\n" );
document.write( "-------------------------------\r\n" );
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document.write( "Bring every factor down on the bottom line\r\n" );
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document.write( "  3·7·a·a      ·b·b·b·b·b·b\r\n" );
document.write( "  3  ·a·a·a·a  ·b·b·b·b·b·b·b·b\r\n" );
document.write( "2  ·7·a·a·a·a·a·b·b·b·b·b·b·b·b\r\n" );
document.write( "-------------------------------\r\n" );
document.write( "2·3·7·a·a·a·a·a·b·b·b·b·b·b·b·b\r\n" );
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document.write( "Multiply all that together and you get:\r\n" );
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document.write( "    42a⁵b⁸\r\n" );
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document.write( "A shorter way is:\r\n" );
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document.write( "1.  Get the LCM of just the coefficients 21,3,and 14, which is 42\r\n" );
document.write( "2.  use the largest power of each letter that occurs in any one \r\n" );
document.write( "    factor.  That's a⁵ and b⁸, for they are the largest\r\n" );
document.write( "    powers of a and b that appear in any of the 3 original expressions.\r\n" );
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document.write( "Edwin
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