What are the ages of her children

Question

                Tom meets a new neighbor, Christina, next door to him.

During the conversation with Christina, Tom asks her, “How many kids do you have?”.

“Three”, replied Christina.

Tom asked, “How old are they?”

                Christina answered: “The product of their ages is 36. The sum of their ages are the same as my house number.”.

                After some time, Tom replied, “I cannot figure it out, I don’t have enough information.”.

                “My apologies, I forgot to tell you that my youngest child likes strawberry milk.”, replied Christina.          

                Tom figured out their ages after her answer and Christina confirmed he was right.

                What are the ages of her children?

Below is the answer:

Below is the combination for the product of 36 and their sums:

• 1 x 2 x 18; 1 + 2 + 18 = 21
• 1 x 3 x 12; 1 + 3 + 12 = 16
• 1 x 4 x 9; 1 + 4 + 9 = 14
• 1 x 6 x 6; 1 + 6 + 6 = 13
• 2 x 2 x 9; 2 + 2 + 9 = 13
• 2 x 3 x 6; 2 + 3 + 6 = 11
• 3 x 3 x 4; 3 + 3 + 4 = 10

Since Tom cannot determine the answer initially, it means at least 2 combinations will arrive at the same sum (which is the house number).

From the above, only (1+6+6) and (2+2+9) will arrive at the same sum of 13.

Christina last statement is that she has a youngest child, so it should be (1+6+6).