We report the discovery of one super-Earth- (TOI-1749b) and two sub-Neptune-sized planets (TOI-1749c and TOI-1749d) transiting an early M dwarf at a distance of 100~pc, which were first identified as planetary candidates using data from the TESS photometric survey. We have followed up this system from the ground by means of multiband transit photometry, adaptive-optics imaging, and low-resolution spectroscopy, from which we have validated the planetary nature of the candidates. We find that TOI-1749b, c, and d have orbital periods of 2.39, 4.49, and 9.05 days, and radii of 1.4, 2.1, and 2.5 \(R_\oplus\), respectively. We also place 95\% confidence upper limits on the masses of 57, 14, and 15 \(M_\oplus\) for TOI-1749b, c, and d, respectively, from transit timing variations. The periods, sizes, and tentative masses of these planets are in line with a scenario in which all three planets initially had a hydrogen envelope on top of a rocky core, and only the envelope of the innermost planet has been stripped away by photoevaporation and/or core-powered mass loss mechanisms. These planets are similar to other planetary trios found around M dwarfs, such as TOI-175b,c,d and TOI-270b,c,d, in the sense that the outer pair has a period ratio within 1\% of 2. Such a characteristic orbital configuration, in which an additional planet is located interior to a near 2:1 period-ratio pair, is relatively rare around FGK dwarfs.