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

Let's first factorize the given number, $243=\underline{3\times 3\times 3}\times 3\times 3$

Here, the 3 x 3 is left after grouping in triplets. Therefore, 243 is not a perfect cube. 

To make it a cube, we need one more 3.

In that case, $243\times 3=\underline{3\times 3\times 3}\times \underline{3\times 3\times 3}=729$ is a perfect cube.
Hence, the smallest natural number by which 243 should be multiplied to make it a perfect cube is 3.