what is the smallest number by which 1372 must be multiplied so that the product is a perfect cube?

1372 = 2X2 X7X7X7

Therefore the smallest no. to be multipied for making the given no perfect cube is = 2 (Ans)

1372=2*7*7*2*7

=2*2*7*7*7

=therefore it must be multipled by 2

(by prime factorization method)1372 = 2 x 2 x 7 x 7 x7

as 2 cannot be grouped into groups of three,so,2 should be multiplied to 1372 in order to make it a perfect cube.

therefore,ans=2 is the smallest number by which 1372 has to be multiplied to be a perfect cube.

hope it helps!thumbs up please!