document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207624>Question 1207624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let $M$ be the least common multiple of $1,$ $2,$ $\dots,$ $12$, $13$, $14$, $15$, $16$.  How many positive divisors does $M$ have? </SPAN>\n" );
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document.write( "M is the LCM of 1, 2, 3, ..., 15, 16<br><BR>\n" );
document.write( "The largest number of factors of 2 in any of those numbers is 4 (2^4=16)<BR>\n" );
document.write( "The largest number of factors of 3 in any of those numbers is 2 (3^2=9)<BR>\n" );
document.write( "No other prime factor less than 16 occurs more than once. So<br><BR>\n" );
document.write( "M = (2^4)(3^2)(5^1)(7^1)(11^1)(13^1)<br><BR>\n" );
document.write( "The number of positive divisors of M is (5*3*2*2*2*2) = 240<br><BR>\n" );
document.write( "ANSWER: 240<br><BR>\n" );
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