Question

The least number
by which 24 must be multiplied to gat a perfect cube​

Answer 1

So the least number by which 24 must be multiplied to get a perfect cube is 9

Step-by-step explanation:

We Have :-

A number :- 24

To Find :-

The least number by which 24 must be multiplied to get a perfect cube

Method Used :-

Prime Factorization

Solution :-

Prime Factorization of 24 is

24 = 2 × 2 × 2 × 3 × 1

In a cube the number should occur in triplets

2 is occuring in triplets

3 is not occuring in triplets

So we multiply 24 by 3 ( 2 times as we need 3 two times to make it a triplet ) to make a triplet

24 × 3 × 3 = 2 × 2 × 2 × 3 × 3 × 3

216 = 2 × 2 × 2 × 3 × 3 × 3

Now it becomes a perfect cube

So the least number by which 24 must be multiplied to get a perfect cube is 9