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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, remain unclear. We present 1.3 mm dust continuum and molecular line observations with the Atacama Large Millimeter/submillimeter Array toward 43 protostellar cores in the Orion molecular cloud complex (lambda Orionis, Orion B, and Orion A) with an angular resolution of similar to 0.'' 35 (similar to 140 au). In total, we detect 13 binary/multiple systems. We derive an overall multiplicity frequency (MF) of 28% +/- 4% and a companion star fraction (CSF) of 51% +/- 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 a higher gas density and Mach number than cores forming single stars. The integral-shaped filament of the 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 GMC has a lower MF and CSF than the Orion B and Orion A GMCs, indicating that feedback from H ii 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.