It is well-known that given two primes $p$ and $q$, $pZ + qZ = Z$ where $Z$ stands for all integers. It seems to me that the set of natural number multiples, i.e. $pN + qN$ also span all natural numbers that are large enough. That is, there exists some $K>0$, such that $$pN + qN = [K,K+1,...).$$
My question is, given $p$ and $q$, can we get a upper bound on $K$?