So I have 2 positive integers a and b, a<b.

And their LCM minus GCD is 143.

Find a and b.

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- Oct 24th 2010, 07:08 AMtepsLeast common multiple - Greatest common divisor
So I have 2 positive integers a and b, a<b.

And their LCM minus GCD is 143.

Find a and b. - Oct 24th 2010, 08:34 AMHappyJoe
The problem is just to find any pair (a,b) for which LCM(a,b) - GCD(a,b) = 143?

You can take a=1, b=144. Their GCD is 1, while their LCM is 144. - Oct 24th 2010, 01:00 PMteps
No, the problem is to find all pairs, forgot to mention that sry. :)

- Oct 24th 2010, 01:40 PMbrennan
do you know the answer - because i think there are infinate answers - or have i been away from amths for so long im making stupid errors?

- Oct 24th 2010, 02:20 PMAlso sprach Zarathustra
LCM(a,b) - GCD(a,b) = 143

LCM(a,b)=k*GCD(a,b), k is some integer.

LCM(a,b) - GCD(a,b) = GCD(a,b) {k-GCD(a,b)}=143

hmmm... - Oct 25th 2010, 05:29 AMteps
- Oct 25th 2010, 05:45 AMAlso sprach Zarathustra