Electronic, magnetic, and transport properties of the noncollinear naturally multilayered compounds LaMn₂Ge₂ and LaMn₂Si₂ are addressed by first-principles calculations based on the density-functional theory. At low temperatures, these systems show a magnetic state with the Mn moments ordered in a conical arrangement (spin spiral) with a ferromagnetic coupling along the c axis and an in-plane antiferromagnetic coupling. The magnetic structures are studied by means of the full-potential linearized augmented-plane-wave method within both the generalized-gradient approximation and the local-density approximation. In both compounds, a conical magnetic state is obtained with energies lower than canted and collinear structures. The trends in the experimentally observed magnetic configuration when replacing Ge by Si are discussed. The origin of the experimentally observed inverse giant magnetoresistance in LaMn₂Ge₂ is traced back to the presence of many noncollinear low-energy magnetic configurations.