Winners from last weeks math problem, and the new problem of the week

Attributions: 

Marble Mayhem

 Fred, Ginger, Julio and Dawn decide to play marbles.  Fred empties his bag of marbles and divides them equally among the four players.  Everyone gets at least one marble.  There is one marble left over.

 At that moment, Jake joins them and asks to play.  They gather up all Fred’s marbles and redivide them among the five kids.  There is still one marble left over.

 Just then, Maria arrives and wants to play so they gather all the marbles again and redistribute them equally six ways.  There is still one marble left over. 

 What is the fewest number of marbles that Fred could have had in his bag?