Young massive star clusters (YMCs, with M $geq$10$^4$ M$_{odot}$) are proposed modern-day analogues of the globular clusters (GCs) that were products of extreme star formation in the early universe. The exact conditions and mechanisms under which YMCs form remain unknown -- a fact further complicated by the extreme radiation fields produced by their numerous massive young stars. Here we show that GC-sized clusters are naturally produced in radiation-hydrodynamic simulations of isolated 10$^7$ M$_{odot}$ Giant Molecular Clouds (GMCs) with properties typical of the local universe, even under the influence of radiative feedback. In all cases, these massive clusters grow to GC-level masses within 5 Myr via a roughly equal combination of filamentary gas accretion and mergers with several less massive clusters. Lowering the heavy-element abundance of the GMC by a factor of 10 reduces the opacity of the gas to radiation and better represents the high-redshift formation conditions of GCs. This results in higher gas accretion leading to a mass increase of the largest cluster by a factor of ~4. When combined with simulations of less massive GMCs (10$^{4-6}$ M$_{odot}$), a clear relation emerges between the maximum YMC mass and the mass of the host GMC. Our results demonstrate that YMCs, and potentially GCs, are a simple extension of local cluster formation to more massive clouds and do not require suggested exotic formation scenarios.
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