  During the transition phase from a prestellar to a protostellar cloud core,
one or several protostars can form within a single gas core. The detailed
physical processes of this transition, however, still remain unclear. We
present 1.3 mm dust continuum and molecular line observations with the Atacama
Large Millimeter/submillimeter Array (ALMA) toward 43 protostellar cores in the
Orion Molecular Cloud Complex ($\lambda$ Orionis, Orion B, and Orion A) with an
angular resolution of $\sim$ 0.35" ($\sim$ 140 au). In total, we detect 13
binary/multiple systems. We derive an overall multiplicity frequency (MF) of
28$\%$ $\pm$ 4$\%$ and a companion star fraction (CSF) of 51$\%$ $\pm$ 6$\%$,
over a separation range of 300-8900 au. The median separation of companions is
about 2100 au. The occurrence of stellar multiplicity may depend on the
physical characteristics of the dense cores. Notably, those containing
binary/multiple systems tend to show higher gas density and Mach number than
cores forming single stars. The integral-shaped filament (ISF) of Orion A giant
molecular cloud (GMC), which has the highest gas density and hosts high-mass
star formation in its central region (the Orion Nebula cluster), shows the
highest MF and CSF among the Orion GMCs. In contrast, the $\lambda$ Orionis
Giant Molecular Cloud (GMC) has a lower MF and CSF than the Orion B and Orion A
GMCs, indicating that feedback from HII regions may suppress the formation of
multiple systems. We also find that the protostars comprising a binary/multiple
system are usually at different evolutionary stages.
