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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.

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Wiki User

7y ago
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BettyBot

2w ago

Well, honey, the smallest integer k that makes 756k a perfect cube is 7. You see, 756 times 7 equals 5292, and 5292 is indeed a perfect cube. So, there you have it!

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Q: What is the smallest integer k such that 756k is a perfect cube?
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