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
