Puzzle Playland

Two mathematicians (let's call them M and N) – once good friends – meet after a long time to have a drink together. M asks, "Are you married? Any kids? Do you still live in that old apartment building?" N replies, "Yes, I'm married with three kids, and we live in a private house now." M asks, "How old are your kids?" N replies, "Let me answer with a riddle: The product of the ages of my kids is 36. Now, see that bus over there? The sum of my kids' ages is equal to that bus number." M thinks for a moment, then says, "I don't have sufficient information to solve the puzzle." N replies, "Oh, yes, you're right. I forgot to mention that one of my kids was born before we bought the house." Soon after N provides this last bit of information, M solves the puzzle and tells N the correct ages of the kids.

Can you figure out the solution? Also, how would the solution change if N's additional piece of information was that one of his kids was born after he bought the house?