Question

Find the smallest perfect square that is exactly divisible by 25,24,and 18.

Answer 1

Answer:

The smallest natural number which is exactly divisible by  25,24  and  18  is the LCM of these three numbers, which is  1800.  

⇒  Any multiple of  1800  is also exactly divisible by  25,24  and  18.  

1800=52×32×23.  

⇒  Multiplying  1800  by  2  would make it the smallest multiple of  1800  which is a perfect square.

⇒3600  is the smallest multiple of  1800  which is a perfect square.

⇒3600  is the smallest perfect square which is exactly divisible by  25,24  and  18

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