Carol 3 numbers

Carol was given three numbers and was asked to add the largest of the three to the product of the other two. Instead, she multiplied the largest with the sum of the other two, but still got the right answer. What is the sum of the three numbers?

Solution:
If the numbers are a,b,c then
ab + c = ac + bc

Doing trial and error, this seems to have multiple solutions, for e.g.
a = b = c = 0
a = c = 1, b = 0
a = b = c = 1
etc.

So I am adding another constraint which was not given in the original question:
These numbers are consecutive natural numbers.
Then you can do a,a+1,a+2.
Now you will get a quadratic equation in a.
Which will give a = 0,-3
And then we choose a = 0 and next 2 numbers are 1,2.

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