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

The Correct Option is B

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