$ABC$ is a triangle with vertices $A=(0,0)$, $B=(36,15)$, and $C=(x,y)$ where both $x$ and $y$ are integers. What is the minimum area of $\triangle ABC$? Provide your answer in the form of \(\frac{k}{m}\) where \(\frac{k}{m}\) is in simplest form. Calculate the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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