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

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