OIMU 2006 Problem 1

Let $m,n$ be positive integers greater than $1$ . We define the sets $P_m=\left\{\frac{1}{m},\frac{2}{m},\cdots,\frac{m-1}{m}\right\}$ and $P_n=\left\{\frac{1}{n},\frac{2}{n},\cdots,\frac{n-1}{n}\right\}$ .

Find the distance between $P_m$ and $P_n$ , that is defined as $$\min\{|a-b|:a\in P_m,b\in P_n\}$$