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What is the smallest integer k such that 756k is a perfect cube?
Wiki User
∙ 7y ago
k = 98.
In the prime factorization (in power format) of a perfect cube, every prime must be to the power of a multiple of 3.
756 = 2^2 x 3^3 x 7
Thus the smallest perfect cube that is a multiple of 756 is 2^3 × 3^3 × 7^3; to obtain this need to multiply 756 by 2^1 × 3^0 × 7^2 = 98
Thus the smallest k to make 756k a perfect prime is k = 98.
Wiki User
∙ 7y ago
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