Question

what smallest number should 7803 be multiplied with so that the product becomes perfect cube

Answer 1

It is 17

by LCM the factors of 7803 are
3*3*3*17*17
So we should multiply with 17

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Answer 2

Find the prime factors:

7803 = 3³ x 17²

Define k:

Let k be the smallest number that needs to be multiplied to get a perfect cube.

Solve k:

For the number to be a perfect cube, the exponent must be in multiples of 3s

7803 = 3³ x 17²

7803k = 3³ x 17³

k = 17

Answer: The number is 17