The author introduces the concept of a level set for establishing the global solution of the multiplicative programming problem \[ \min \prod^m_{i=1} f_i(x)\text{ subject to }x\in M,\tag{1} \] where \(M\subset \mathbb{R}^n\) is a nonempty convex set, \(m\geq 2\). Main result: It is not necessary to know the set of all efficient solutions of the multicriteria \(\min[f_1(x),\dots,f_m(x)]\). A level set algorithm for finding a global solution of the multiplicative programming problem (1) is presented. Finally, an illustrative example is proposed.