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 ____

Question

TestHub · Accepted Answer

​ L . C . M ( p , q ) = 2 2 ⋅ 3 4 ⋅ 5 2 p = 2 a 1 ​ ⋅ 3 b 1 ​ ⋅ 5 c 1 ​ q = 2 a 2 ​ ⋅ 3 b 2 ​ ⋅ 5 c 2 ​ ⇒ max { a 1 ​ , a 2 ​ } = 2 ⇒ 5 w a ys ⇒ max { b 1 ​ , b 2 ​ } = 4 ⇒ 9 w a ys ⇒ max { c 1 ​ , c 2 ​ } = 2 ⇒ 5 w a ys ∴ K = 3 2 ⋅ 5 2 c anb ee x p resse d a s 1 ⋅ 3 2 ⋅ 5 2 , 3 2 ⋅ 5 2 ​

Mathematics - Permutation & Combination Question with Solution | TestHub

Options:

Doubts & Discussion