Question

What is the least perfect square which is divisible by 24 30 and 60?

Answer 1

Step 1: LCM of 24 , 30 and 60 = 120

so 120 is the least no which is divisible by all 24 , 30 and 60

Step 2: factors of 120 will be 2^3 * 3 * 5

so the least perfect square, which is divisible by 24, 30 and 60 will be
(2^3 * 3 * 5) x ( 2 * 3 * 5 ) = 3600



3600

Answer 2

Answer: 3600 is the least perfect square number which is divisible by 24,30 and 60.

Explanation:

Since we have given that

The numbers are 24,30 and 60.

We need to find the least perfect square.

First we find the L.C.M. of 24, 30 and 60 .

So, L.C.M. of 24, 30 and 60 = 120

But 120 is not a perfect square because:

120=2×2×2×3×5

Since 2,3 and 5 has no pair.

We will multiply with 2,3,and 5.

So, it becomes,

2×2×2×3×5×2×3×5

=3600

Hence, 3600 is the least perfect square number which is divisible by 24,30 and 60.