Question

What is the smallest number by which $243$should be multiplied to get a perfect cube?

Answer 1

$243=\underset{–}{3\times 3\times 3}\times \underset{–}{3\times 3}$
The prime factor $3$ does not appear in a group of three the second time.

So, $243$ is not a perfect cube.

To make it perfect cube we need one more $3$.
Hence, the smallest number by which $243$ must be multiplied so that the product is a perfect cube is $3$.