Seven elevators

Puzzle

The superintendent of an apartment building tells you that his building has seven elevators. Each elevator stops on at most 6 floors. He also tells you that you can get to any one floor from any other floor without changing elevators (if you take the right elevator). What is the largest number of floors that the building could have?

Meta-puzzle

In general, if a building has <math>m</math> elevators which can each visit at most <math>n</math> floors, how many floors could the building have if you must be able to get from any one floor to any other floor by using a single elevator?

References

Problem Solving by Thomas DeFranco and Charles Vinsonhaler.