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

1.	The least perfect square, which is divisible by each of 21, 36 and 66, is:1. 2314442. 2143443. 2134444. 214434
Answer» 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.

The least perfect square, which is divisible by each of 21, 36 and 66, is:1. 2314442. 2143443. 2134444. 214434

Answer» 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.

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