Transforming high-order mode Laguerre-Gaussian beams in the far-field using a 127-actuator deformable mirror controlled by a stochastic parallel gradient descent algorithm is presented. As a phase shift of half wave exists between every neighboring lobes of high-order mode Laguerre-Gaussian beams, there are multiple lobes in the far-field. The suitable beam radius related to the aperture size of the deformable mirror is discussed. Three system performance metrics are evaluated, and encircled energy is preferred. Simulation results show that it is possible to compensate for the phase shifts and other phase aberrations of a high-order mode Laguerre-Gaussian beam and achieve a single bright lobe with this approach. Transforming the far-field intensity distribution of high-order mode Laguerre-Gaussian beams into Gaussian and super Gaussian distributions are also investigated.