What is the smallest perfect square which is completely divisible by each of 16, 18 and 36?

144

The correct answer is Option 1: 144

To find the smallest perfect square that is completely divisible by 16, 18, and 36, we need to follow two main steps: find the Least Common Multiple (LCM) of the numbers and then ensure that the result is a perfect square.

16 = 2 × 2 × 2 × 2

18 = 2 × 3× 3

36 = 2 × 2 × 3 × 3

LCM of 16, 18 and 20 = 2 × 2 × 2 × 2 × 3 × 3 = 144

A number is a perfect square if all the exponents in its prime factorization are even. In the prime factorization of 144 (${2^}^4\times 3^{^2}$), both exponents (4 and 2) are even. Therefore, 144 is already a perfect square (12^2)