Young massive clusters (YMCs) are the most intense regions of star formation in galaxies. Formulating a model for YMC formation whilst at the same time meeting the constraints from observations is highly challenging however. We show that forming YMCs requires clouds with densities $gtrsim$ 100 cm$^{-3}$ to collide with high velocities ($gtrsim$ 20 km s$^{-1}$). We present the first simulations which, starting from moderate cloud densities of $sim100$ cm$^{-3}$, are able to convert a large amount of mass into stars over a time period of around 1 Myr, to produce dense massive clusters similar to those observed. Such conditions are commonplace in more extreme environments, where YMCs are common, but atypical for our Galaxy, where YMCs are rare.
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