Help with my daugther's grade 3 question.

a= b+1 b= c+1 abc = 120

I know the solution is a= 6, b= 5, and c= 4 but i cannot calculate it logically without guessing.

abc= 120 (c+2)(c+1)c=120

c3+3c2+2c=120

How do I get C?

Is there a way to calculate it?