Help with a math brain teaser?

A man and woman are on an airplane chatting about their families. The woman says that she has 3 children, the age of each child is a counting number, the product of their ages is 72, and the sum of their ages is the same as the flight number. The man checks his ticket for the flight number, does a bit of figuring, and says that he needs more information to determine the ages. The woman then points to the peanuts that they are munching on and says that the oldest is allergic to peanuts. The man then tells the woman the correct ages of her children. What are the ages and how do you figure it out?