Unfortunately $A$ cannot be $0$

Given that $m, n \in \mathbb{Z^{+}}$ , $m \leq 6008$ and $\large{A = \Big(3 - \frac{m}{n}\Big)}$ find the smallest positive number $A$ .

If $\large{A_{min} = \Big(\frac{a}{b}\Big)^c}$ for $a, b, c \in \mathbb{Z}$ insert the number $(a + b + c)$ as your answer.