Question

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

Answer 1

To find the least perfect square that is divisible by 24,30 and 60, first find the LCM (Least Common Multiple)

By factorization method:

24 = 3*8 = 2^3 * 3

30 = 2 * 3 * 5

60 = 4*15 = 2^2 * 3 * 5

LCM (24,30,60) = 2^3 * 3 * 5

Now, we can see that the above LCM is not a perfect square number.

But if the LCM is multiplied by a 2,3&5 we will get a perfect square number which is divisible by each of 24,30,60

LCM = 2^3*3*5=== 2^3*2*3*3*5*5 = 2^4 * 3^2 * 5^2 = 3600

Hence, 3600 is the least perfect square that  is divisible by each of 24,30,60