Find all pairs of integers a, b such that their GCD and LCM are 14 and 168 respectively.
a x b = gcd(a,b) x lcm(a,b) (useful?)
The Attempt at a Solution
Maybe, maybe not. What does it tell you?a x b = gcd(a,b) x lcm(a,b) (useful?)
That looks correct. Is it useful?bphysics said:a x b = 2352...
You don't know how to find all of the solutions to a x b = 2352?bphysics said:it's somewhat useful, gives me one more piece of information, but i can't see the way to solve it...
Ah. So you do know how to solve the problem, you're just fishing for other methods.bphysics said:i can find pairs, but some of them would be incorrect ex. a = 1 and b = 2352. i was wondering if there would be a better way or shortcut without having to go through all the pairs.
Er, what is there to explain? You know how to find all the solutions to a x b = 2352, so now we're just imposing some of the information from the original problem to streamline our work.bphysics said:wait a dividing lcm(a, b)?
can you explain more?
I thought that's what I was doing...bphysics said:could you lead me though it?
Hrm. I expected three answers. (But I could be wrong)bphysics said:so are the answers (14, 168) and (42, 56)?