The least perfect square number completely divisible by 4, 5, 9 and 12 is:

Correct option is A

Given:

We need to find the least perfect square number that is completely divisible by 4, 5, 9, and 12.

Solution:

First, we find the prime factorization of each number:

4 = $$2^2$$​​

5 $$= 5^1$$​​

9 $$= 3^2$$​​

12 = $$2^2 \times 3^1$$​​

LCM(4,5,9,12) = $$2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180$$​

The LCM of 180 is $$2^2 \times 3^2 \times 5^1$$​.

To make it a perfect square, we need to ensure all exponents are even.

The exponent of 5 is 1, so we need to multiply by another 5 to make the power of 5 even.

Thus, we multiply the LCM by 5:

Least perfect square = 180 × 5 = 900

The square root of 900 is:

​$$\sqrt{900} = 30$$​

Thus, 900 is a perfect square.

The least perfect square number completely divisible by 4, 5, 9, and 12 is 900.