Find all pairs of integers (m, n) such that their greatest common divisor is 1155 and their least common multiple 86625.
This problem confuses me quite a bit. I just don't see how i could find these numbers. I am not supposed to use a calculator, so I'm guessing it is done with prime factorization. Any help on which direction to start in would be appreciated.
Find all pairs of integers (m, n) such that their GCD is 1155 and their LCM is 86,625.
There are two basic solutions:
And, of course, the roles of and can be reversed.
Thank you very much for the help. One more question, how did you go about finding that second pair of solution? I'm curious as to why;
m = 3^2 * 5^2 * 7 * 11
n = 3 * 5 * 7 * 11
would not be a valid pair. Both would be less then 86625 and greater then 1155 wont they?