Mind Boggling, Seemingly Impossible Age Problem

Number Theory Level pending

One Mathematician presents the following problem to another mathematician: "I have three daughters. The product of their ages is 72, and the sum of their ages is the number of the house across the street (he points towards the house across the street). What is each daughters' age?" The second mathematician says "it is impossible!" At this point, the first mathematician then relents, providing the final piece of information: "my eldest daughter loves chocolate." The second mathematician now says "Ok, now I know each of your three daughter's ages."

What are the three daughter's ages?

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