Question 1207624
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M is the LCM of 1, 2, 3, ..., 15, 16<br>
The largest number of factors of 2 in any of those numbers is 4 (2^4=16)
The largest number of factors of 3 in any of those numbers is 2 (3^2=9)
No other prime factor less than 16 occurs more than once. So<br>
M = (2^4)(3^2)(5^1)(7^1)(11^1)(13^1)<br>
The number of positive divisors of M is (5*3*2*2*2*2) = 240<br>
ANSWER: 240<br>