The European Solar Telescope (EST) will be a 4-meter diameter world-class facility, optimized for studies of the magnetic coupling between the deep photosphere and upper chromosphere. It will specialize in high spatial resolution observations and therefore it has been designed to incorporate an innovative built-in Multi-Conjugate Adaptive Optics system (MCAO). It combines a narrow field high order sensor that will provide the information to correct the ground layer and a wide field low order sensor for the high altitude mirrors used in the MCAO mode. One of the challenging particularities of solar AO is that it has to be able to correct the turbulence for a wide range of observing elevations, from zenith to almost horizon. Also, seeing is usually worse at day-time, and most science is done at visible wavelengths. Therefore, the system has to include a large number of high altitude deformable mirrors. In the case of the EST, an arrangement of 4 high altitude DMs is used. Controlling such a number of mirrors makes it necessary to use fast reconstruction algorithms to deal with such large amount of degrees of freedom. For this reason, we have studied the performance of the Fractal Iterative Method (FriM) and the Fourier Transform Reconstructor (FTR), to the EST MCAO case. Using OCTOPUS, the end-to-end simulator of the European Southern Observatory, we have performed several simulations with both algorithms, being able to reach the science requirement of a homogeneous Strehl higher that 50% all over the 1 arcmin field of view.