Find the least perfect square which is exactly divisible by each of 6, 15 and 20.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 900
The number must be a multiple of the LCM, and in a perfect square every prime appears an even number of times.
LCM \(=2^{2}\times3\times5=60\)
Primes with an odd power: 3, 5
Multiply the LCM by them: \(60\times15=900=30^{2}\)
The least perfect square is 900.
Why the other options are incorrect
Option (1) 400 — Incorrect. 400 is a perfect square but is not divisible by 6.
Option (3) 3600 — Incorrect. 3600 is a perfect square divisible by all of them, but 900 is smaller.
Option (4) 60 — Incorrect. 60 is not a perfect square.