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In this letter, we investigate a beam placement problem to determine the optimal beam center position that maximizes the minimum transmission rate of users within a spot beam for a multicast transmission in low-Earth-orbit satellite communications. We make a system model for satellite beam placement and formulate an optimization problem that maximize the minimum transmission rate of ground nodes (GNs). Then, we propose a gradient ascent algorithm to calculate the optimal beam center position. The simulation results show that the proposed scheme optimally determines the position of the beam center and maximizes the minimum rate of GNs according to various satellite parameters. [ABSTRACT FROM AUTHOR]