We recently introduced the Kaczmarz algorithm for solving the atmospheric tomography problem in multiconjugate adaptive optics (MCAO). This iterative method solves the problem significantly faster than the standard matrix vector multiplication. We present the algorithm as well as an extension, which includes the effects of laser guide stars, such as the cone effect, tip/tilt indetermination, and spot elongation. We show that we can successfully cope with these effects and that the algorithm is suited for an MCAO system for the future generation of extremely large telescopes.