72

Prime Factorization:

⇒ 72 = 2 × 2 × 2 × 3 × 3

= 2³ × 3²

There are only two 3’s.

∴ 72 is not a perfect cube.

To make it a perfect cube, we have to multiply with 3.

⇒ 72 × 3 = 2 × 2 × 2 × 3 × 3 × 3

⇒ 216 = 2³ × 3³

= 6³ which is a perfect cube.

∴ The smallest number by which 72 must be multiplied to obtain a perfect cube is 3.