Check sibling questions

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

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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

Find the smallest square number which is divisible by each of the numbers - Part 2

 

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

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

 

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.