The least number by which 72 be

3

Resolving 72 into prime factors, we get

72=2 x 2 x 2 x 3 x 3

Grouping the factors in triplets of equal factors, we get

72 = (2 x 2 x 2) x 3 x 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 x 2 x 2 x 3 x 3 x 3, which is a perfect cube.

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