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We calculate the Longitudinal Magnetoresistance in the Extreme Quantum Limit (ħΩ_c ⪡ k_BT) for a nondegenerate n-type InSb sample at low temperatures when the dominant energy and momentum loss mechanisms are the el-acoustic phonon and the el-ionized impurity interactions. The magnetic field dependence of the effective mass which is due to the nonparabolic nature of the conduction band as well as the energy and magnetic field dependence of the relaxation time are incorporated in the analysis. Analytical results are presented for both nondegenerate and degenerate samples when individual scattering mechanisms are operative. In general nonparabolicity causes an enhancement in the Longitudinal Magnetoresistance and changes the nature of its magnetic field dependence as compared to the case of a parabolic conduction band.