# Thread: Least common multiple - Greatest common divisor

1. ## Least 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.

2. 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.

3. No, the problem is to find all pairs, forgot to mention that sry.

4. 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?

5. 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...

6. Originally Posted by Also 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...
You mean LCM(a,b) - GCD(a,b) = GCD(a,b) (k-1)=143=13*11, thank you from here on i make 4 cases, and get that:
(a,b)={(22,77);(11,154);(39,52);(13,156);(9,16);(1 ,144);(143,246)}

7. Originally Posted by teps
You mean LCM(a,b) - GCD(a,b) = GCD(a,b) (k-1)=143=13*11, thank you from here on i make 4 cases, and get that:
(a,b)={(22,77);(11,154);(39,52);(13,156);(9,16);(1 ,144);(143,246)}
Typo, thanks...

Good-job btw.