It is well known that laser beams spread as they propagate through free space due to natural diffraction, and that there is additional spreading when optical waves propagate through atmospheric turbulence. Previous studies on Gaussian beams have mainly involved the lowest order mode (zero order). The study of higher order mode Gaussian beams has involved Hermite-Gaussian and Laguerre-Gaussian beams for rectangular and cylindrical geometry, respectively. These studies have developed expressions for the field and intensity in free space, in addition to developing new definitions of beam size in the receiver plane for the higher order modes. We calculate the mean intensity of higher order mode Gaussian beams propagating through atmospheric turbulence, and, based on previously developed definitions for beam radius, we calculate the additional beam spreading due to random media. It is shown that higher order mode Gaussian beams experience less percentage of additional broadening due to atmospheric fluctuations than the zero-order mode beams.