Lagrangian Cloud Model (LCM) is a mixed Eulerian/Lagrangian approach to atmospheric large eddy simulation (LES), with two‐way coupling between Eulerian dynamics and thermodynamics and Lagrangian microphysics. Since Lagrangian representation of microphysics does not suffer from numerical diffusion in the radius space and solves full droplet growth equations, it may be considered an alternative for the bin approach. This paper documents the development of LCM to include collision/coalescence processes. The proposed algorithm maps Lagrangian parcels collision/coalescence events on the specified two‐dimensional grid, with the first dimension spanning aerosol radius and the second dimension spanning the cloud droplet radius. The proposed approach is capable of representation of aerosol activation, deactivation, transport inside the droplets, and processing by clouds and in the future may be used to investigate details of these processes. As an illustration, LCM with collision/coalescence is used to investigate effects of aerosols on cloud microphysics and dynamics for a marine stratocumulus cloud. Two extreme cases are considered that represent low and high aerosol concentrations. It is shown that the aerosol type significantly affects cloud microphysics as well as cloud dynamics. In agreement with previous studies, a larger entrainment rate is simulated for the high aerosol concentration. For the low aerosol concentration, intense collision/coalescence and drizzle modify the aerosol size distribution, reducing the concentration in the dry radius range of 0.02 to 0.2 μm and increasing the concentration for dry radii larger than 0.3 μm.