Find the smallest square number which is divisible by each of the numbers

Let’s take an example to do it

What is the smallest square number which is divisible by 2, 4, 6?

We saw that

  Smallest number divisible by 2, 4, 6 = LCM of 2, 4, 6

But, we need to find the smallest square number

So,

• We check if LCM is a perfect square
• If its not, then we find the smallest number multiplied to it so that it becomes a perfect square

LCM of 2, 4, 6

LCM of 2, 4, 6 = 2 × 2 × 3

        = 12

Now, checking if 12 is a perfect square or not

Checking if 12 is a perfect square

We see that ,

  12 = 2 × 2 × 3

Since 3 does not occur in pairs,

It is not a perfect square

So, we need to find a number to multiply to make pairs

We multiply by 3

So, our number becomes

  12 × 3 = 2 × 2 × 3 × 3

So, it becomes a perfect square

∴ Smallest square number which is divisible by 2, 4, 6 is 36

Thus, we can write

  Smallest square number divisible by 2, 4, 6

     = LCM of 2, 4, 6

    OR

          Multiple of LCM