Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube.
100
100
Prime Factorization:
⇒ 100 = 2 × 2 × 5 × 5
There are only two 2’s and two 5’s.
Hence, 100 is not a perfect cube.
To make it a perfect cube, we have to multiply it with 2 × 5 = 10.
⇒ 100 × 2 × 5 = 2 × 2 × 2 × 5 × 5 × 5
⇒ 1000 = 23 × 53
= 103 which is a perfect cube.
∴ The smallest number by which 100 must be multiplied to obtain a perfect cube is 10.
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