Question

Find the smallest number by which $243$ must be multiplied to obtain a perfect cube.

Answer 1

Prime factorizing $243$, we get,

$243=3\times 3\times 3\times 3\times 3=3^5$.

We know, a perfect cube has multiples of $3$ as powers of prime factors.
Here, number of $3$'s is $5$.

So we need to multiply another $3$ in the factorization to make $243$ a perfect cube.

Hence, the smallest number by which $243$ must be multiplied to obtain a perfect cube is $3$.