A mathematician and a lady strike conversation during a flight.

The lady asks the mathematician to guess the age of her three daughters. Mathematician, being unable to answer the questions, asks for some hint(s).

The lady replies: The product of their ages is 36.
Still unable to answer, mathematician asks for another hint.

Hint 2: The sum of their ages is equal to your (i.e. mathematician’s) seat number.
Mathematician still cann’t answer the question.

Final hint: My (i.e. the lady’s) youngest daughter has blue eyes.

Listening to the final hint, mathematician is able to answer the question.
Can you too? How?