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Let m be the least common multiple of 1,2,3, ..., 20. How many positive divisors does m have?

 Mar 24, 2019
 #1
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LCM 20

 

1, 2 , 3, 2^2, 5, 6, 7, 2^3, 3^2, 10, 11, 12, 13, 14, 15, 2^4, 17, 18, 19 , 20  =

 

5 * 7 * 3^2 * 11 * 13 * 2^4 * 17 * 19   

 

It will have

2 * 2 * 3 * 2 * 2 * 5 * 2 * 2  = 

 

960 positive divisors

 

 

cool cool cool

 Mar 24, 2019

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