Number of pairs of positive integers (p, q) whose LCM (Least common multiple) is 8100, is "K". Then number of ways of expressing K as a product of two coprime numbers is ____

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L.C.M ( p , q ) = 2 2 3 4 . 5 2 P = 2 a 4 ​ 3 b 1 ​ . 5 c 1 ​ q = 2 a 2 ​ 3 b 2 ​ 5 c 2 ​ ⇒ max { a 1 ​ , a 2 ​ } = 2 ⇒ 5 ways ⇒ max { b 1 ​ , b 2 ​ } = 4 ⇒ 9 ways ⇒ max { c 1 ​ , c 2 ​ } = 2 ⇒ 5 ways ∴ K = 3 2 . 5 2 can be expressed as 1. 3 2 5 2 , 3 2 . 5 2

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