Question

Find the smallest perfect Square that is exactly divisible by each of the following number (1) 6, 9 and 15​

Answer 1

Answer:

This has to be done in two steps.

First find the smallest common multiple and then find the square number needed. The least number divisible by each one of 6, 9 , and 15 is their LCM The LCM of 6,9, and 15 is  2 × 3 × 3 × 5 = 90

Prime factorisation of 90 is 90 =  2 ×   3× 3  × 5  

We see that prime factors 2 and 5 are not in pairs.

Therefore 90 is not a perfect square.

In order to get a perfect square each factor of 90 must be paired. So we need to make pairs of 2 and 5 Therefore 90 should be multiplied by  2 × 5 i.e., 10  

Hence the required square number is  90 × 10 = 900.

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