So why don't you copy String::LCSS and modify it to work on words instead of characters? The implementation finds the longuest common substring (LCSS) of characters, but the algorithm can just as easily find the LCSS of words.

Update: Turns out String::LCSS is buggy and unmaintained. It doesn't work for inputs of the form lcss("b", "ab"); (like your example) and other inputs. It's apparently using an inefficient algorithm too, according to one of the bug reports (which actually provides an implementation of a better algorithm).