Q. 104.3( 110 Votes )

Find the smallest square number that is divisible by each of the numbers 8, 15 and 20

Answer :

We know that the number that is perfectly divisible by each of the numbers 8, 15, and 20 is their LCM.

Therefore,


LCM of 8, 15, and 20 is:


2 × 2 × 2 × 3 × 5 =120


Here, prime factors 2, 3, and 5 do not have their respective pairs.


Therefore, 120 is not a perfect square


Therefore, 120 should be multiplied by 2 × 3 × 5, i.e. 30, to obtain a perfect square


Hence,


The required square number = 120 × 2 × 3 × 5


= 3600

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