In recent years, many organisations use high-performance computing clusters to, within a few days, perform complex simulations and calculations that otherwise would have taken years, even lifetimes, with a single computer. However, these high-performance computing clusters can be very expensive to purchase and maintain. For developing countries, these factors are viewed as barriers that will slow them in their quest to develop the necessary computing platforms to solve complex, real-world problems. From previous studies, it was unclear if an off-the-shelf personal computer (single computer) and low-cost computing clusters are feasible alternatives to high- performance computing clusters for smaller scientific problems. The aim of this study was to investigate this gap in literature since according to our knowledge, this kind of study has not been conducted before. The study made use of High Performance Linpack benchmark applications to collect quantitative data comparing the time-to-complete, operational costs and computational efficiency of a single computer, a low-cost computing cluster and a high-performance cluster. The benchmark used the HPL main algorithm and matrix sizes for the n x n dense linear system ranged from 10 000 to 60 0000. The costs of the low-cost computing cluster were kept to the minimum (USD4000.00) and the cluster was constructed using locally available computer hardware components. In this study for the cases we studied, we found that a low-cost computing cluster was a viable alternative to a high-performance cluster if the environment requires that costs be kept to a minimum. We concluded that for smaller scientific problems, both the single computer and low- cost computing cluster was better alternatives to a high-performance cluster. However, with large scientific problems and where performance and time are of more importance than costs, a high- performance cluster is still the best solution, offering the best efficiency for both theoretical energy consumption and computation.