document.write( "Question 256386: What is the value of the positive integer n for which the least common multiple of
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Algebra.Com's Answer #188654 by Edwin McCravy(20055) $\"\"$ $\"About$

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What is the value of the positive integer n for which the least common multiple of
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document.write( "The divisors of 36 are 1,2,3,4,6,9,12,18,36\r\n" );
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document.write( "500 more than these are \r\n" );
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document.write( "501,502,503,504,506,509,512,518,536\r\n" );
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document.write( "The LCM of n and 36 must be among these\r\n" );
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document.write( "All multiples of 36 end with an even digit, so that\r\n" );
document.write( "narrows the LCM of n and 36 down to\r\n" );
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document.write( "502,504,506,512,518,536\r\n" );
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document.write( "504 is the only one of those which is a multiple of 36\r\n" );
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document.write( "So 4 must be the GCD and 504 must be the LCM.\r\n" );
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document.write( "the factors of 504 are  \r\n" );
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document.write( "2*2*2*3*3*7   \r\n" );
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document.write( "and the factor of 36 are\r\n" );
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document.write( "2*2*3*3\r\n" );
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document.write( "since the GCD of 36 and n is 4, n must have 2 factors of 2.\r\n" );
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document.write( "In addition to those two 2 factors that n has in common \r\n" );
document.write( "with 36, n must also have another 2 factor as well\r\n" );
document.write( "as a 7 factor, since 504 does and 36 doesn't. n doesn't need any 3 \r\n" );
document.write( "factors because 36 has two 3 factors.  So n has the two 2 factors \r\n" );
document.write( "in common with 36 and an additional 2 factor.  That's three factors of \r\n" );
document.write( "2 and one 7 factor, and so n = 2*2*2*7=56\r\n" );
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document.write( "Edwin

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