Question

By what least number should 648be multiplied to get a perfect cube? How?

Answer 1

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3
In the prime factors, only 2 and 3 are present. 2 form a triplet (there are three 2s), while there are four 3s.To be a perfect cube, all prime factors should be in multiples of 3. Therefore, to make 648 a perfect cube, it has to be multiplied by 3 × 3 = 9 (so that there will be six 3s in total).

P.S. You can also multiply by $\frac{1}{3}$, which is smaller or by $\frac{1}{648}$, which is even smaller, but the officially accepted answers are integers, unless they specify otherwise.

Answer 2

648=2*2*2*3*3*3*3
To make it a perfect cube, either it has to be multiplied by 9 or 1/3