Question

The least number by which 72 be multiplied to make it a perfect cube is ______.

Answer 1

The least number by which 72 be multiplied to make it a perfect cube is 3.

Explanation:

Resolving 72 into prime factors, we get

72 = 2 × 2 × 2 × 3 × 3

Grouping the factors in triplets of equal factors, we get

72 = (2 × 2 × 2) × 3 × 3

We find that 2 occurs as a prime factor of 72 thrice, but 3 occurs as a prime factor only twice.

Thus, if we multiply 72 by 3, 3 will also occurs as a prime factor thrice and the product will be 2 × 2 × 2 × 3 × 3 × 3, which is a perfect cube.

Hence, the least number, which should be multiplied with 72 to get perfect cube, is 3.