Problem Solving - 47

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

Answer: B

990 is a multiple of n! implies it must contain all the prime factors of 990
Largest prime factor of 990 is 11 implies n! must have 11 as a factor

Now since n! = 990x where x is integer it implies it can have prime factors more than 11 but not less than 11

Thus least possible value of n is thus 11