Find the smallest number by which $53240$ must be multiplied to make it a perfect cube.

Given: A number $53240$.

To do: To find the smallest number by which 53240 must be multiplied to make it a perfect cube.

Given number: $53240$.

Prime factorization of the number:

$53240=\underline{2\times2\times2}\times5\times\underline{11\times11\times11}$

As known that a cube of a number consists of three numbers.

in the above factors we find that there is a triplet of $2$ and $11$, but not of $5$.

To make a triplet for $5$ we need two more $5$

$=5\times5$

$=25$

Thus, the smallest number is $25$ by which 53240 must be multiplied to make it a perfect cube.