Using the high-resolution near-infrared adaptive optics imaging from the NaCo instrument at the Very Large Telescope, we report the discovery of a new binary companion to the M-dwarf LP 1033-31 and also confirm the binarity of LP 877-72. We have characterised both the stellar systems and estimated the properties of their individual components. We have found that LP 1033-31 AB with the spectral type of M4.5+M4.5 has a projected separation of 6.7$pm$1.3 AU. Whereas with the spectral type of M1+M4, the projected separation of LP 877-72 AB is estimated to be 45.8$pm$0.3 AU. The binary companions of LP 1033-31 AB are found to have similar masses, radii, effective temperatures, and log $g$ with the estimated values of 0.20$pm$0.04 $rm{M}_{odot}$, 0.22$pm$0.03 $rm{R}_{odot}$, 3200 K, 5.06$pm$0.04. However, the primary of LP 877-72 AB is found to be twice as massive as the secondary with the derived mass of 0.520$pm$0.006 $rm{M}_{odot}$. The radius and log $g$ for the primary of LP 877-72 AB are found to be 1.8 and 0.95 times that of the secondary component with the estimated values of 0.492$pm$0.011 $rm{R}_{odot}$ and 4.768$pm$0.005, respectively. With an effective temperature of 3750$pm$15 K, the primary of LP 877-72 AB is also estimated to be $sim$400 K hotter than the secondary component. We have also estimated the orbital period of LP 1033-31 and LP 877-72 to be $sim$28 and $sim$349 yr, respectively. The binding energies for both systems are found to be $gt$10$^{43}$ erg, which signifies both systems are stable.
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