By which least number should 1323 be multiplied to get a perfect cube?

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answer is C.

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Detailed Solution

It is given that 1323 is multiplied by the smallest number to get a perfect cube.
Find the prime factorization of 1323.

3132334413147749771

Prime factorization of 1323 =

3 × 3 × 3 ¯ × 7 × 7 × 1.

From the prime factorization of 1323, clearly, factor 3 occurs in a triplet while 7 doesn’t occur in a triplet.
For a product to be a perfect cube all prime factors should exist in a triplet. So, to complete the triplet number, it needs to be multiplied by 7.
Hence, the smallest number to be multiplied by 1323 to make the product a perfect cube is 7.
Thus, option (3) is correct.

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