If the GCD is not 1, any integer that is not a multiple of the GCD will be unobtainable with the given coins; and the converse can be viewed as a consequence of Schur's theorem.
If the GCD is not 1, any integer that is not a multiple of the GCD will be unobtainable with the given coins, and therefore there is no largest such integer. The converse can be viewed as a consequence of Schur's theorem.