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Multiplicative programming problems are difficult global optimization problems known to be NP-hard. In this paper we propose a method for approximately solving convex multiplicative programming problems. This work is based on our previous work “An approximation algorithm for convex multiobjective programming problems”. We show, by slightly changing the algorithm, that our method can be used to solve convex multiplicative programming problems. We provide an example that shows that our method has computational advantage compared with Benson's outcome space branch and bound outer approximation algorithm.