Question

The least perfect square, which is divisible by each of 21, 36 and 66 is:

• A. 214344
• B. 213444
• C. 214434
• D. 231444

Answer 1

Answer: (B)

213444

Answer 2

Prime factorization of$21 = 3 \times7$
Prime factorization of$36 = 2 \times 2 \times 3 \times 3 \text{ or } 22 \times 32$
Prime factorization of$66 = 2 \times 3 \times11$
Maximum of all the prime exponents that exist in the numbers above will be
LCM$= 22 \times 32 \times 7 \times 11$
→ The least number, which is divisible by 21,36, and 66 is$22 \times 32 \times 7 \times 11$
In a perfect square, always exponent of each prime is always even, so
In order to find the least perfect square, we will make each exponent even
$22 \times 32 \times 72 \times 112 = 213444$
Therefore, the least perfect square, which is divisible by 21, 36, and 66 is 213444.
The correct answer is (B): 213444