What is the smallest number by which 68600 must be multiplied to get a perfect cube?

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answer is B.

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Detailed Solution

It is required to find the smallest number by which 68600 must be multiplied to get a perfect cube.
Utilizing prime factorization, express the given integer as a prime factor product.

⇒ 68600 = 2 × 2 × 2 × 5 × 5 × 7 × 7 × 7 = 23 × 52 × 73

68600 is not a perfect cube since factor 5 does not contain triples.
The result of multiplying 68600 by 5 is a number that forms a perfect cube.
Therefore, 5 is the least number that needs to be multiplied to 68600 to produce a perfect cube.
Hence, option 2 is correct.

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