Laguerre-Gaussian (LG) beams are used in many research fields, including microscopy, laser cavity modes, and optical tweezing. We developed a holographic method to generate pure LG modes (amplitude and phase) with a binary amplitude-only digital micromirror device (DMD) as an alternative to the commonly used phase-only spatial light modulator. The advantages of such a DMD include very high frame rates, low cost, and high damage thresholds. We have shown that the propagating shaped beams are self-similar and their phase fronts are of helical shape as demanded. We estimate the purity of the resultant beams to be above 94%.