June Question of the Month for Algebra Two

Alice, Beth, and Charlene start climbing a staircase, each with her left foot on step 1 and then her right foot on the next consecutive step.  Alice climbs one step at a time, Beth two steps at a time, and Charlene three steps at a time.  Each lands on the top step with her left foot.  Compute the minimum number of stairs in the staircase.