Find the least number by which 6250 should be multiplied, so that it becomes a perfect cube.

Correct option is C

Given:

Number = 6250

Solution:

Prime factorization of 6250:

6250 = $$625 \times 10 = (5^4) \times (2 \times 5) = 2^1 \times 5^5$$​​

For a perfect cube:

Power of 2 is 1 → needs two more to make 3.

Power of 5 is 5 → needs one more to make 6 (multiple of 3).

So, we multiply by:

​$$2^2 \times 5^1 = 4 \times 5 = 20$$​​

20 is the least number by which 6250 should be multiplied to make it a perfect cube.