Question

Find the smallest number by which the following number must be multiplied to obtain a perfect cube:$72$

Answer 1

Step 1: Find the prime factors

Given number, $72$

$72=2\times 2\times 2\times 3\times 3$

Step 2: Find the smallest number multiplied to obtain perfect cube

By assorting the factors in triplets of equal factors, $72=(2\times 2\times 2)\times 3\times 3$

Here, $3$ cannot be arranged into triplets of equal factors.

$\therefore$ We will multiply $72$ by $3$ to get a perfect cube.

Hence, the smallest number by which $72$ must be multiplied to obtain a perfect cube is $3$.