Q. The least perfect square which is divisible by 3, 4, 5, 6, 8 is
a) 900
b) 3600
c) 1200
d) 2500
Correct Answer: b) 3600
Question from UPPSC Prelims CSAT 2025
Explanation:
A number divisible by 3, 4, 5, 6, and 8 must be a multiple of their LCM. LCM(3,4,5,6,8) = 2^3 * 3 * 5 = 120.
For the least perfect square multiple of 120, make all prime exponents even: 120 = 2^3 * 3^1 * 5^1 → multiply by 2 * 3 * 5 to get 2^4 * 3^2 * 5^2 = (60)^2 = 3600.
Thus, 3600 is the smallest perfect square divisible by all the given numbers.