Question

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

Answer 1

Answer:

3

Step-by-step explanation:

if 3 is multiplied to 72 you will get 216 which is a perfect cube of 6

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Answer 2

Answer:

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

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

When 72 is multiplied by 3, then 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.