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least possible value of n

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least possible value of n

by abhi332 » Wed Feb 24, 2010 11:18 am
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?

A) 10
B) 11
C) 12
D) 13
E) 14

ANS: B
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by Pedros » Wed Feb 24, 2010 11:29 am
abhi332 wrote:If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?

A) 10
B) 11
C) 12
D) 13
E) 14

ANS: B
The product of all integers from 1 to N inclusive is a multiple of 990

Prime factorization of 990 yields 2,3,3,5, and 11.

so the numbers from 1 to N must include 11 . So N's least possible value is 11
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