Question

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

100

Answer 1

2	100
2	50
5	25
5	5
	1

100 = 2 × 2 × 5 × 5

Here, two 2s and two 5s are left, which are not in a triplet. To make 100 a cube, we require one more 2 and one more 5.

Then, we obtain

100 × 2 × 5 = 2 × 2 × 2 × 5 × 5 × 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 × 5 = 10.