A survey of 30 nearby M6.0-M7.5 dwarfs with K_s < 12 mag utilizing the Hokupa`a adaptive optics system at the Gemini North Telescope has discovered three new binary systems. All three systems have separations between 012 and 029 (3-10 AU) with similar mass ratios (q > 0.8, ΔK_s < 0.7). This result gives further support to the suggestion that wide (a > 20 AU), very low mass (M_tot < 0.185 M) binary systems are exceedingly rare or perhaps even nonexistent. The semimajor axis distribution of these systems peaks at ~5 AU, tighter than more massive M and G binary distributions, which have a broad peak at separations of ~30 AU. We find a sensitivity-corrected binary fraction in the range 5% for M6.0-M7.5 stars with separations a > 3 AU. This binary frequency is less than the ~32% measured among early M dwarfs over the same separation range. Two of the low-mass binaries are probable Hyades open cluster members based on proper motions, cluster membership probabilities, radial velocities, and near-IR photometry. LP 415-20 has the distinction of being the tightest (3.6 AU) multiple system ever spatially resolved in the cluster, and the companions of LP 415-20 and LP 475-855 are among the least massive objects ever resolved in the Hyades, with estimated masses of 0.081 and 0.082 M.