The least perfect square, which is divisible by each of 21, 36 and 66 is
2023
The least perfect square, which is divisible by each of 21, 36 and 66 is
- A.
213414
- B.
213424
- C.
213444
- D.
213434
Attempted by 78 students.
Show answer & explanation
Correct answer: C
Key idea: find the LCM of the numbers and then make all prime exponents even to get a perfect square.
Factorise the numbers: 21 = 3 × 7, 36 = 2^2 × 3^2, 66 = 2 × 3 × 11.
LCM collects the highest powers: LCM = 2^2 × 3^2 × 7^1 × 11^1 = 2772.
To be a perfect square, each prime exponent must be even. Currently 2 and 3 have even exponents, but 7 and 11 have exponent 1. Multiply by 7 × 11 = 77 to make those exponents even.
Therefore the least perfect square divisible by 21, 36 and 66 is 2772 × 77 = 213444.
Answer: 213444