What is the least square number which is exactly divisible by 2, 3, 10, 18 and 20?

Question: What is the least square number which is exactly divisible by 2, 3, 10, 18 and 20?
Solution:

The least or smallest number which is exactly divisible by 2, 3, 10, 18, and 20 is the LCM of 2, 3, 10, 18, and 20.

LCM (2, 3, 10, 18, 20) = 180

180 = 2² × 3² × 5

So, to become a perfect square 180 needs to be multiplied by 5.

Now, the least square number which is exactly divisible by 2, 3, 10, 18 and 20

⇒ 180 × 5 = 900

∴ The least-square number which is exactly divisible by 2, 3, 10, 18, and 20 is 900.