Question

Find the smallest number by which $72$ must be multiplied to obtain a perfect cube.

Answer 1

Prime factorising $72$, we get,

$72=2\times 2\times 2\times 3\times 3$ $=2^3\times 3^2$.

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

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

So we need to multiply another $3$ in the factorization to make $72$ a perfect cube.

Hence, the smallest number by which $72$ must be multiplied to obtain a perfect cube is $3$.