If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n? Choose one.
A) 10 B) 11 C) 12 D) 13 E) 14
You need to primarily find the primes of 990:   2,3,3,5,11   The integer must contain all these primes   By knowing 11 is an prime, we know the answer can be B,C,D or E as these all contain 11.   11=1,2,3,4,5,6,7,8,9,10,11   11 contains the 2,3,5 and 11 explicitly and the second 3 comes from the 6 (2*3), therefore the answer is 11.   This is because we know a number that contains all the primes of 990 will be a multiple of 990.   ANSWER:11
<result>B</result>
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?