#### Question

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

100

#### Solution

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.

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Find the Smallest Number by Which the Following Number Must Be Multiplied to Obtain a Perfect Cube. 100 Concept: Cubes - Smallest Multiple that is a Perfect Cube.

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