Question

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

Answer 1

hope this helps..........^-^

Answer 2

Answer:

Step 1: We will find the prime factors of 1372

by prime factorisation method

1372 = 2 × 2 × 7 × 7 × 7

Step 2: Find the least number

If we see, the prime factors of 1372, 7 is in

the group of 3 i.e. it makes a cube but 2 is

not in a group of 3 i.e. it is not making a

cube.

•2 is the smallest number by which 1372 must be multiplied so that the product becomes a perfect cube.

Let's check:

→1372 x The least number

⇒1372 × 2

⇒ 2744

→$\sqrt[3]{2744 } = 14$

Hence, proved.