The smallest perfect square number divisible by each of 6 and 12 is:

To find the smallest perfect square divisible by both 6 and 12:
Find the LCM of 6 and 12:
The Least Common Multiple (LCM) of 6 and 12 is 12.
Any number divisible by both 6 and 12 must be a multiple of 12.

Find the prime factorization of 12:

12=2×2×3=2
2
×3
1

Make it a perfect square:
For a number to be a perfect square, the exponents of all its prime factors must be even numbers.
To make 12 a perfect square, we must multiply it by the missing factor to complete the pairs, which is 3:

Smallest perfect square=12×3=36
Checking the options, 36 is a perfect square (6
2
) and is perfectly divisible by both 6 and 12.