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A three-dimensional(3D)free-parameter multiple-relaxation-time lattice Boltzmann method for high speed compressible and low speed incompressible flows is presented.In this approach the transformation matrix is constructed according to the irreducible representation basis functions of SO(3)group.Equilibria of the nonconserved moments are chosen so as to recover the compressible Navier-Stokes equations through the Chapman-Enskog analysis.The sizes of the discrete velocities are flexible.The influence of model parameters on the numerical stability is analyzed,and some reference values of parameters are suggested.To validate the performance of the proposed model,well-known benchmark problems are simulated.The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results.