Correct Answer - Option 3 : 213444
Given:
The least perfect square, which is divisible by 21, 36 and 66
Concept used:
A number which is divisible by 21, 36, and 66 will be the LCM of these numbers
Calculation:
Prime factorization of 21 = 3 × 7
Prime factorization of 36 = 2 × 2 × 3 × 3 or 22 × 32
Prime factorization of 66 = 2 × 3 × 11
Maximum of all the prime exponents that exist in the numbers above will be
LCM = 22 × 32 × 7 × 11
⇒ The least number which is divisible by 21,36, and 66 is 22 × 32 × 7 × 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 × 32 × 72 × 112 = 213444
∴ The least perfect square which is divisible by 21, 36, and 66 is 213444.
