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ABSTRACT We study the physical drivers of slow molecular cloud mergers within a simulation of a Milky Way-like galaxy in the moving-mesh code arepo, and determine the influence of these mergers on the mass distribution and star formation efficiency of the galactic cloud population. We find that 83 per cent of these mergers occur at a relative velocity below 5 km s−1, and are associated with large-scale atomic gas flows, driven primarily by expanding bubbles of hot, ionized gas caused by supernova explosions and galactic rotation. The major effect of these mergers is to aggregate molecular mass into higher-mass clouds: mergers account for over 50 per cent of the molecular mass contained in clouds of mass M > 2 × 106 M⊙. These high-mass clouds have higher densities, internal velocity dispersions and instantaneous star formation efficiencies than their unmerged, lower mass precursors. As such, the mean instantaneous star formation efficiency in our simulated galaxy, with its merger rate of just 1 per cent of clouds per Myr, is 25 per cent higher than in a similar population of clouds containing no mergers.