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

32.jpg

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

33.jpg

 

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

34.jpg

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

 

  1. Chapter 6 Class 8 Squares and Square Roots
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.