Vortices are topologically stable singularities at the center of a swirl of energy. Optical vortices are conventionally formed using diffractive optics or by bespoke optical elements. We report room temperature integrated lasers directly generating and multiplexing coherent beams carrying arbitrarily large orbital angular momenta (OAM). The OAM beams are created using two-dimensional topological-rings formed by circular boundaries between topologically distinct photonic materials that naturally radiate vortices in the third dimension. We also demonstrate the planar multiplexing of OAM beams using concentric lasers. Our experimental demonstration reveals a subtle connection between topological matter and topological light and provides opportunities in microscopy, metrology, high-capacity communications, and quantum information processing.