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
A. 10
B. 11
C. 12
D. 13
E. 14
tmmyc wrote:The question states the product of 1 to n inclusive is a multiple of 990. This means this product will be 990 multiplied by "other stuff".
First, find the prime factors of 990: 2 3 3 5 11
From here, we know that n must be at least 11.
Let's assume n is 11.
Product of all integers from 1 to n where n = 11: 1*2*3*4*5*6*7*8*9*10*11
Here we see that 990's prime factors are all covered in the product above: 2, 3, 5, and 11 are present. The extra 3 can be taken from the 6. The rest of the product is the "other stuff".
Hence 11 is the least possible value of n.
