This paper presents a method to determine continuous aperture sources or efficient arrays to accurately produce Laguerre-Gaussian (LG) modes traveling towards a target. The method is based on numerical filtering that solves an inverse source problem. The resulting continuous source distribution is then discretized into a minimized equivalent array by constructing a generalized Gaussian quadrature. Because LG modes are widely known for their well-defined orbital angular momentum (OAM) characteristics, the ability to generate pure LG modes is of great importance to OAM-based wireless communications.