A well-known logic problem goes something like this: A census-taker (Andy) and a man (Bob) are having a conversation:

Andy: How many children 18 or younger do you have? Bob: 3 Andy: How old are they? Bob: Well, the product of their ages is 72, and the sum of their ages is the same as my address. Andy: I still can’t determine their ages. Bob: Oh, I should mention that my oldest child is older than either of my other 2 children. Andy: Ok, now I know how old your children are.

Instead of 72, what is the next largest number that Bob could have said, such that the rest of the conversation could have proceeded the same way?