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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