Hello,
So initially I thought there might some cases like there are in questions regarding divisors, range, odd, even etc. However, there wasn't any such case.

I tried simulating the above problem for a = 1-20, b =1-20, c= 1-20. The maximum possible answer was 3 and minimum was 3 so I was sure simulation was enough. I tried my best to derive some relation but was unable to do so.

So in this way, you could think about solving the problem and just simulate the whole process to solve it.