Do you actually mean the largest that cannot be written as a nonnegative integer combination of the two values? That would be the Frobenius number.
FrobeniusNumber[{7, 11}]
(* Out[875]= 59 *)
If this is what you had in mind, then the wording was such that W|A would not have much of a chance, since the phrase "divisible by" is used quite incorrectly. If you meant something else, I defer to the response by Murray Eisenberg.