A Monday Puzzle

To start the week, a puzzle I've adapted directly from a Quora thread:
https://www.quora.com/What-is-the-best-math-puzzle-ever

The format will be familiar to many of you.
I've given the answer farther below, but without explanation, so if you need that, you can go to the link, find the problem, and check the responses there.

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Two math grads run into each other at the shopping mall, having not seen each other in 20 years. Their conversation proceeds like this:

M1:   How have you been?

M2:   Great! I got married and now have 3 daughters.

M1:   Wonderful... how old are they?

M2:   Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there.

M1:   Sure, ok... er wait... Hmmm, I still don’t know their ages.

M2:   Ohh sorry, the oldest one just started piano lessons.

M1:  Ahh, now I know!

Question: how old are the 3 daughters???

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answer:
3, 3, and 8