How Old Are the Children?

'How Old Are the Children?' printed from https://nrich.maths.org/

A student in a maths class was trying to get some information from her teacher.

Sally :	"How many chidren have you got, Mrs Smith?"
Mrs Smith:	"Three"
Sally:	"How old are they?"
Mrs Smith:	"If you multiply their ages together, it comes to 72"
Sally:	"That doesn't give us enough information, Mrs Smith"
Mrs Smith:	"If you add the ages you get the number of this room"
Sally:	"That still doesn't give us enough information, Mrs Smith"
Mrs Smith:	"The youngest is called Amanda"
Sally:	"Thank you. Now we know how old they are !"

Well, how old are they?