This paper presents an optimization method for computing an optimum lookup table size for two well-known look up table elementary function approximation methods; Symmetric Table Additional Method (STAM) and Multipartite Table Method (MTM). Using a discrete optimization algorithm called Leapfrogging, this paper utilizes a method to find the best decomposition of the coefficients to optimize look up table sizes. The resulting designs can easily be utilized for any approximation for functions up 24-bits of precision with significantly smaller requirements for lookup table sizes. Results show that the proposed optimized method is able to achieve higher memory efficiency than the best existing MTM. For the sine function, the optimized method saves 85.29 percent of memory for 16-bit accuracy and 53.89 percent for 24-bit accuracy when comparing to the best existing result obtained by the unified Multipartite Table Method.