If m and n are positive integer, and 1800m=n^3, what is the least possible value of m?	Choose the correct choice from the following answers.
A) 2 B) 3 C) 15 D) 30 E) 45

Rationale: 1800 * m = n ^ 3 m = n ^ 3 / 1800 = n ^ 3 / ( 3 ^ 2 * 5 ^ 2 * 2 ^ 3 ) so n has to be 3 * 5 * 2 so that n ^ 3 is divisible by 1800 . so m = ( 2 * 3 * 5 ) ^ 3 / ( 3 ^ 2 * 5 ^ 2 * 2 ^ 3 ) m = 15 answer : c
Answer: C