Find the smallest perfect square number which is divisible by 4, 9 and 10 ?

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Solution:

⇨ 4 = 2 x 2 x 1

⇨ 9 = 3 x 3 x 1

⇨ 10 = 2 x 5 x 1

⇨L.C.M (4,9,10) = 2 x 2 x 3 x 3 x 5 x 1

⇨L.C.M (4,9,10) = 180

⇨ Now prime factors of 180 will be

⇨ 180 = 2 x 2 x 3 x 3 x 5

⇨ Here we can see that there is no pair of factor 5.

⇨ So we multiply 180 by 5 to get the smallest perfect square divisible by 4, 9, 10

⇨ 180 x 5 = 900