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Modern day wireless networks are increasingly supporting various civilian applications that require high bandwidth for successful operation. In such cases, proper bandwidth utilization is essential for good network performance. In this paper, we address the problem of routing a given traffic demand matrix in a multi-hop wireless mesh network such that the total network load is fairly distributed amongst various wireless links. Using lexicographic optimization, we develop a polynomial time multi-path load balanced routing scheme that achieves leximax minimization and distributes the total network load fairly in a min-max sense. We use linear programming to formulate our problem and perform extensive simulations to highlight the performance of our routing scheme in achieving optimal load balance whilst satisfying user requirements.