Find the smallest number by which 100 must be multiplied to obtain a perfect cube.

$100=2\times 2\times 5\times 5$

Here prime factors 2 and 5 do not appear in a group of three. Therefore, 100 is not a perfect cube. 

To make it a cube, we need one more 2 and one more 5.

In that case, $100\times 2\times 5=\underline{2\times 2\times 2}\times \underline{5\times 5\times 5}=1000$ is a perfect cube.
Hence, the smallest natural number by which 100 should be multiplied to make it a perfect cube is $2\times 5=10$.