We present high-resolution 3D smoothed particle hydrodynamics simulations of the formation and evolution of protostellar discs in a turbulent molecular cloud. Using a piecewise polytropic equation of state, we perform two sets of simulations. In both cases, we find that isolated systems undergo a fundamentally different evolution than members of binary or multiple systems. When formed, isolated systems must accrete mass and increase their specific angular momentum, leading to the formation of massive, extended discs, which undergo strong gravitational instabilities and are susceptible to disc fragmentation. Fragments with initial masses of 5.5, 7.4 and 12 Mjup are produced in our simulations. In binaries and small clusters, we observe that due to competition for material from the parent core, members do not accrete significant amounts of high specific angular momentum gas relative to isolated systems. We find that discs in multiple systems are strongly self-gravitating but that they are stable against fragmentation due to disc truncation and mass profile steeping by tides, accretion of high specific angular momentum gas by other members and angular momentum being redirected into members’ orbits. In general, we expect disc fragmentation to be less likely in clusters and to be more a feature of isolated systems.