What's the Largest?

Number Theory Level pending

A seafood store carries 2-sized tins of oysters. One contains 5 oysters and the other contains 7 oysters. Bill wishes to feed his guests exactly 1 oyster each and have none left over. What is the largest number of guests he can't feed?

Some of the numbers that fit the criteria are 1, 2, 3, 4, 6, 8, 9, 11... Find the largest.

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