Context. Observations of young multiple star systems find a bimodal distribution in companion frequency and separation. The origin of these peaks has often been attributed to binary formation via core and disc fragmentation. However, theory and simulations suggest that young stellar systems that form via core fragmentation undergo significant orbital evolution. Aims. We investigate the influence of the environment on the formation and orbital evolution of multiple star systems, and how core fragmentation contributes to the formation of close (20-100 AU) binaries. We use multiple simulations of star formation in giant molecular clouds and compare them to the multiplicity statistics of the Perseus star-forming region. Methods. Simulations were run with the adaptive mesh refinement code RAMSES with sufficient resolution to resolve core fragmentation beyond 400 AU and dynamical evolution down to 16.6 AU, but without the possibility of resolving disc fragmentation. The evolution of the resulting stellar systems was followed over millions of years. Results. We find that star formation in lower gas density environments is more clustered; however, despite this, the fractions of systems that form via dynamical capture and core fragmentation are broadly consistent at ∼40% and ∼60%, respectively. In all gas density environments, we find that the typical scale at which systems form via core fragmentation is 103-3.5 AU. After formation, we find that systems that form via core fragmentation have slightly lower inspiral rates (∼10- 1.68 AU yr- 1 measured over the first 10 000 yr) compared to dynamical capture (∼10- 1.32 AU yr- 1). We then compared the simulation with the conditions most similar to the Perseus star-forming region to determine whether the observed bimodal distribution can be replicated. We find that it can be replicated, but it is sensitive to the evolutionary state of the simulation. Conclusions. Our results indicate that a significant number of low-mass close binaries with separations from 20-100 AU can be produced via core fragmentation or dynamical capture due to efficient inspiral, without the need for a further contribution from disc fragmentation.