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Radiative transfer modelling is part of many astrophysical simulations and is used to make synthetic observations and to assist analysis of observations. We concentrate on the modelling of the radio lines emitted by the interstellar medium. In connection with high-resolution models, this can be significant computationally challenge. Our goal is a line radiative transfer (RT) program that makes good use of multi-core CPUs and GPUs. Parallelisation is essential to speed up computations and to enable the tackling of large modelling tasks with personal computers. The program LOC is based on ray-tracing and uses standard accelerated lambda iteration (ALI) methods for faster convergence. The program works on 1D and 3D grids. The 1D version makes use of symmetries to speed up the RT calculations. The 3D version works with octree grids and, to enable calculations with large models, is optimised for low memory usage. Tests show that LOC gives results that are in agreement with other RT codes to within ~2%. This is typical of code-to-code differences, which often are related to different interpretations of the model set-up. LOC run times compare favourably with those of Monte Carlo codes. In 1D tests, LOC runs were by up to a factor ~20 faster on a GPU than on a single CPU core. In spite of the complex path calculations, up to ~10 speed-up was observed also for 3D models using octree discretisation. GPUs enable calculations of models with hundreds of millions of cells, as encountered in the context of large-scale simulations of interstellar clouds. LOC shows good performance and accuracy and and is able to handle many RT modelling tasks on personal computers. Being written in Python, with the computing-intensive parts implemented as compiled OpenCL kernels, it can also a serve as a platform for further experimentation with alternative RT implementations.