We investigate properties of lower hybrid drift waves (LHDWs) near and inside the electron diffusion regions in 17 magnetopause and 9 magnetotail reconnection events using Magnetospheric MultiScale (MMS) mission observations. Our analysis show that LHDW type depend on the electron beta, as electron beta increases LHDWs become more electromagnetic in nature. The energy transfer from electromagnetic fields to particles is higher in electrostatic LHDWs and it is largely in parallel direction. Linear dispersion analysis shows that electrostatic LHDWs are perpendicular propagating while electromagnetic waves propagate in oblique directions and the normalized wavenumber of all LHDW types falls within 0.5 to 0.8 range. A simple estimate on the LHDW nonlinear saturation suggests possibly important roles played by these waves in supporting reconnection electric field.