One of the challenging tasks in LTE baseband receiver design is synchronization, which determines the symbol boundary and transmitted frame start-time, and performs cell identification. Conventional algorithms are based on correlation methods that involve a large number of multiplications and thus lead to high receiver hardware complexity and power consumption. In this paper, a hardware-efficient synchronization algorithm for frame timing based on K-means clustering schemes is proposed. The algorithm reduces the complexity of the primary synchronization signal for LTE from 24 complex-multiplications, currently best known in the literature, to just 8. Simulation results demonstrate that the proposed algorithm has negligible performance degradation with reduced complexity relative to conventional techniques.