Mathematician daughters age problem?

Problem:
Two old friends(Mathematicians) meet each other after 20 years.Lets call them A,B.
A says to B: “how have you been?”
B says: “Great! I got married and I have three daughters now”
A says: “Really? how old are they?”
B says: “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..”
A says: “I still don’t know”
B says: “The oldest one just started to play the piano”
A says: “my oldest is the same age!”

Solution:

This is simple mathematical problem which can be solved by applying simple logical reasoning in the case of ambiguity.
After first clue A couldn't answer the question just because there might be two sets of three numbers which produce product of 72 and the sum of numbers in both the sets is equal.
After simple calculation we can reduce on two following two sets where sum of numbers is equal.
(8,3,3) & (6,6,2)
In second case two elder kids are of same age, so you cannot pick an “oldest”. Answer is (8,3,3) hence.