What is the least square number exactly divisible by 5, 6, 9, 15, 18 and 20?
Correct Answer: Option B
The numbers that are perfectly divisible by all of 5, 6, 9, 15, 18 and 20 are their LCM and the multiples of the LCM.
5 = 5
6 = 2 × 3
9 = 3 × 3
15 = 3 × 5
18 = 2 × 3 × 3
20 = 2 × 2 × 5
∴ LCM of 5, 6, 9, 15, 18, 20 = (2 × 2 × 3 × 3 × 5) = 180
∴ smallest multiple of 180 which is a perfect square = (2 × 2 × 3 × 3 × 5) × 5 = 900
∴ required number = 900
Download our app for free and access thousands of MCQ questions with detailed solutions