Select Page

If r, s, t are prime numbers & p, q are positive integers such that the LCM of p, q is r²t²s⁴, then the number of ordered pair (p,q) is

by | Feb 26, 2022 | Uncategorized | 0 comments

(Q). If r, s, t are prime numbers & p, q are positive integers such that the LCM of p, q is r²t²s⁴, then the number of ordered pair (p,q) is?
Solution:-
Since r, s, t are prime numbers.
∴ selection of p & q will be done in following ways:-

pq∴ total number of ways to select r = 3 + 3 - 1 = 5 ( counted twice)selection of s as under: - p q s s, s, s, s, s s, s, s, s, s s ∴ total number of ways to select s = 5 + 5 -1 = 9(p,q → s, s counted twice) selection of t as under: - p q t t, t, t t, t, t t∴ total number of ways to select t = 3 + 3 - 1 = 5(p, q → t, t counted twice)∴ required num ber of ordered pair (p, q) is = 5×9×5 Answer

Submit a Comment

Your email address will not be published. Required fields are marked *

Captcha loading...