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Modern data centres consume large amounts of power resulting in high levels of carbon dioxide emission. The data centre is a virtual environment in which the workload is performed by virtual machines. A widely used technique to decrease data centre power consumption is to consolidate the virtual machines using a minimal number of physical servers. The authors propose a two-stage method to solve the virtual machine consolidation problem in cloud data centres. The proposed method is programmed in C# to evaluate it and to perform modelling using Google cluster-usage traces. The proposed method enables powering off nearly fifty percent of the previously selected physical servers by using an acceptable number of migrations of virtual machines.