We present updated results of a high-resolution , magnitude limited ( K _ { s } < 12 mag ) imaging survey of nearby low-mass M6.0-M7.5 field stars .
The observations were carried out using adaptive optics at the Gemini North , VLT , Keck II , and Subaru telescopes .
Our sample of 36 stars consists predominantly of nearby ( \lesssim 30 pc ) field stars , 5 of which we have resolved as binaries .
Two of the binary systems , 2MASSI J0429184-312356 and 2MASSI J1847034+552243 , are presented here for the first time .
All 5 discovered binary systems have separations between 0 \farcs 08 - 0 \farcs 53 ( 2 - 9 AU ) with similar mass ratios ( q > 0.8 , \Delta K _ { s } < 1 mag ) .
This result supports the hypothesis that wide ( a > 20 AU ) very low-mass ( M _ { tot } < 0.19 M _ { \sun } ) binary systems are rare .
The projected semimajor axis distribution of these systems peak at \sim 5 AU and we report a sensitivity-corrected binary fraction of 9 _ { -3 } ^ { +4 } \% for stars with primaries of spectral type M6.0-M7.5 with separations \gtrsim 3 AU and mass ratios q \gtrsim 0.6 .
Within these instrumental sensitivities , these results support the overall trend that both the semimajor axis distribution and binary fraction are a function of the mass of the primary star and decrease with decreasing primary mass .
These observations provide important constraints for low-mass binary star formation theories .