Question

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

72

Answer 1

2	72
2	36
2	18
3	9
3	3
	1

72 = 2 × 2 × 2 × 3 × 3

Here, two 3s are left that are not in a triplet. To make 72 cubes, one more 3 is required.

Then, we obtain

72 × 3 = 2 × 2 × 2 × 3 × 3 × 3 = 216 is a perfect cube.

Hence, the smallest natural number by which 72 should be multiplied to make it a perfect cube is 3.