document.write( "Question 618063: Find the number of positive integers that are divisors of at least one of 10^10, 15^7, 18^11. \n" ); document.write( "
Algebra.Com's Answer #388886 by Edwin McCravy(20060)\"\" \"About 
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document.write( "10^10 = (2*5)^10 = (2^10)(5^10)\r\n" );
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document.write( " 15^7 = (3*5)^7  =  (3^7)(5^7)\r\n" );
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document.write( "18^11 = (2*3^2)^11 = (2^11)(3^22)\r\n" );
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document.write( "Any positive integer of the form \r\n" );
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document.write( "2^p*3^q*5^r \r\n" );
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document.write( "will be a factor of at least one of those if\r\n" );
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document.write( "0 <= p <= 11,  0 <= q <= 22, and 0 <= r <= 10 \r\n" );
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document.write( "There are 12 choices for p, times 23 choices for q, \r\n" );
document.write( "times 11 choices for r.\r\n" );
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document.write( "Answer = 12*23*11 = 3036 divisors of at least one \r\n" );
document.write( "of 10^10, 15^7, 18^11.\r\n" );
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document.write( "Edwin
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