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Find the smallest square number which is divisible by each of the numbers
Last updated at August 12, 2026 by Teachoo
Smallest number multiply or divide to get perfect square
Ganita Prakash Class 8 - Part 1, 2
Chapter 1 Class 8 - A Square and a Cube (Ganita Prakash)
- Introduction
- Square Numbers
- Perfect Squares - and its Properties
- Perfect Squares - and its Patterns
- Square Root
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Smallest number multiply or divide to get perfect square
- Estimating Square Root
- Figure it out - Page 10, 11
- Cubic Numbers
- Perfect Cubes - and its Properties
- Perfect Cubes - and its Patterns
- Cube Root
- Smallest number multiply or divide to get perfect cube
- A pinch of History
- Figure it out - Page 16, 17
Transcript
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 36 = 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
