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Cloud data centres are critical business infrastructures and the fastest growing service providers. Detecting anomalies in Cloud data centre operation is vital. Given the vast complexity of the data centre system software stack, applications and workloads, anomaly detection is a challenging endeavour. Current tools for detecting anomalies often use machine learning techniques, application instance behaviours or system metrics distribu- tion, which are complex to implement in Cloud computing environments as they require training, access to application-level data and complex processing. This paper presents LADT, a lightweight anomaly detection tool for Cloud data centres that uses rigorous correlation of system metrics, implemented by an efficient corre- lation algorithm without need for training or complex infrastructure set up. LADT is based on the hypothesis that, in an anomaly-free system, metrics from data centre host nodes and virtual machines (VMs) are strongly correlated. An anomaly is detected whenever correlation drops below a threshold value. We demonstrate and evaluate LADT using a Cloud environment, where it shows that the hosting node I/O operations per second (IOPS) are strongly correlated with the aggregated virtual machine IOPS, but this correlation vanishes when an application stresses the disk, indicating a node-level anomaly.