Calculate the least perfect square, which is exactly divisible by each of 2, 5, 7, 8 and 10.

Correct option is D

Given:

We need to find the least perfect square that is exactly divisible by 2, 5, 7, 8, and 10.

Concept Used:

LCM (Least Common Multiple): The required number must be a perfect square and a multiple of the LCM of the given numbers.

Solution:

Prime factorizations: $$2 = 2^1, \quad 5 = 5^1, \quad 7 = 7^1, \quad 8 = 2^3, \quad 10 = 2^1 \times 5^1$$​​

Taking the highest power of each prime: LCM = $$2^3 \times 5^1 \times 7^1 = 280$$​​

To make it a perfect square, all prime powers must be even.

Multiply by$$2\times5\times7 = 70$$​ to make all exponents even.

= 280 × 70 = 19600