SOLUTION: Find the number of positive integers that are divisors of at least one of 10^10, 15^7, 18^11.

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Question 618063: Find the number of positive integers that are divisors of at least one of 10^10, 15^7, 18^11.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
10^10 = (2*5)^10 = (2^10)(5^10)

 15^7 = (3*5)^7  =  (3^7)(5^7)

18^11 = (2*3^2)^11 = (2^11)(3^22)

Any positive integer of the form 

2^p*3^q*5^r 

will be a factor of at least one of those if

0 <= p <= 11,  0 <= q <= 22, and 0 <= r <= 10 

There are 12 choices for p, times 23 choices for q, 
times 11 choices for r.

Answer = 12*23*11 = 3036 divisors of at least one 
of 10^10, 15^7, 18^11.

Edwin