"79 fish works though"

So does 25, 52, and all numbers of the form 27n - 2 where n is any integer.

For then:
Fisherman 1 leaves 2/3 (27n - 3) = 18n - 2 fish;
Fisherman 2 leaves 2/3 (18n - 3) = 12n - 2 fish;
Fisherman 3 leaves 2/3 (12n - 3) =   8n - 2 fish.