Question

Find the smallest number by which $3087$ must be multiplied so that the product is a perfect cube.

Answer 1

Prime factorising $3087$, we get,

$3087=7\times 7\times 7\times 3\times 3$

$=7^3\times 3^2$.

We know, a perfect cube has multiples of $3$ as powers of prime factors.

Here, number of $7$'s is $3$ and number of $3$'s is $2$.

So we need to multiply another $3$ to the factorization to make $3087$ a perfect cube.

Hence, the smallest number by which $3087$ must be multiplied to obtain a perfect cube is $3$.