If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x=2^i∗3^k∗5^m∗7^p, then i + k + m + p = Choose the correct option
A) 4	B) 7	C) 8	D) 11	E) 12

Rationale: "here the idea is to go expressing each factor from one to eight , decomposed into its primes : 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 1 * 2 * 3 * ( 2 * 2 ) * 5 + ( 2 * 3 ) * 7 * ( 2 * 2 * 2 ) = 2 ^ 7 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1 then i = 7 k = 2 m = 1 p = 1 i + k + m + p = 11 correct answer d"
Answer: D