Find the least perfect square, which is divisible by each of 22, 36 and 66.

The answer is 4356=66^2.

Step-by-step explanation:

We find following prime factorization:

22=2*11

66=2*3*11

36=2^2+3^2.

We know that the least perfect square must be divisible by 66. We see also that the square of 66 is divisible by 36 from factorization and 22 divides 66 too.

Now we need to find the least perfect square that is divisible by 66. That is 66^2=4356, which we can explain as follows:

prime factors of 66 are 2, 3 and 11 and 66 is a square free number, hence the least perfect square 66 is divisible by is 66^2=4356.