My New Favourite Brainteaser

I just had my mind blown by the most diabolical brainteaser. At first glance it seems impossible to figure out, but there is actually a fairly logical way to solve it. I wish I could say that I solved it, but I have to admit to giving up.  Here it is:

Two mathematicians are at the pub having a beer and a yarn. One of them says “Hey, I bet you $5 you can’t work out the ages of my three daughters.”
The other one says “Is that so? I’ll take your bet.”
“Okay, so the product of their ages is 72. The sum of their ages is the same as the number of the house across the street.”
The second mathematician thinks about it for a moment, then says “You haven’t given me enough information to solve the riddle.”
“Okay, my eldest daughter loves chocolate.”
The second mathematician says “Too easy”, gives the answer and takes his $5.

How old are the daughters?

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