# Thread: If r,s,t are prime nos. and p,q are the positive integers ....

1. ## If r,s,t are prime nos. and p,q are the positive integers ....

A liitle help!

If r,s,t are prime nos. and p,q are the positive integers such that the LCM of p,q is (r^2)*(t^4)*(s^2) then find the number of ordered pair (p,q)...just wanted to verify the answer....

2. Originally Posted by findmehere.genius
A liitle help!

If r,s,t are prime nos. and p,q are the positive integers such that the LCM of p,q is (r^2)*(t^4)*(s^2) then find the number of ordered pair (p,q)...just wanted to verify the answer....

If $\displaystyle P:=\{p\in\mathbb{N}\;;\;p\,\,a\,\,prime\}$ , and if $\displaystyle \displaystyle{n=\prod\limits_{p\in P}}p^{a_p}\,,\,\,m=\prod\limits_{p\in P}p^{b_p}}$ , with

$\displaystyle a_p=b_p=0$ for all but a finite number of primes, then $\displaystyle LCM(n,m)=\prod\limits_{p\in P}p^{max(a_p,b_p)}$ .

Thus in our case, either p or q will have to be divided by each of those primes to the corresp. power.

For example, $\displaystyle (r^2t^4s^2,1),\, (rt^3s^2,r^2t^4),\, (rt^3s^2,r^2t^4s)$ are some of the

wanted pairs. Now you find them all.

Tonio

3. thanks tonio, it was exactly what we( I and a friend) were trying, answer gives us 225...!