Problem:
Let and be distinct prime numbers, where is not considered a prime. Which of the following is the smallest positive perfect cube having as a divisor?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If is a divisor of cube , then must have and as primes in its factorization. Moreover, the exponents of and in the factorization must be multiples of and they must be at least as great as and , respectively ( being the exponents of in ). Thus is the smallest such cube.