Given two positive integers `a,b`

what is the minimal integer `n`

, so that there exist two positive integers `u,v`

for which `n=au=av`

?

It is easy to verify that `n=ab/gcd(a,b)`

.

But what happens if instead of requiring `au=bv`

, or `|au-bv|`

≤`0`

, we require that `|au-bv|`

≤`k`

for some number k?

That is, given two positive integers `a,b`

, what are the minimal integers `u,v`

for which `|au-bv|`

≤`k`

, for some `k`

? If there's no direct formula, is there an easy way to find `u,v`

?