Balance the chemical equation
\mbox{K} \mbox{O}_{4} + \mbox{C} \mbox{O}_{2} \longrightarrow \mbox{K}_5 \mbox{C}_3 \mbox{O}_2 + \mbox{O}_2

and give your answer in lowest terms. That is, the coefficients should all be integers that do not all share a common factor.

You can earn partial credit on this problem.