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Accurate future workload prediction is an essential step for proactive resource allocation and efficient provisioning in cloud computing environments. Deep learning strategies have proven successful for this task, but they face challenges due to the high dimensionality of monitoring data, extensive preprocessing requirements, and computational overhead. In this paper, we propose a hybrid framework that integrates autoencoders for workload compression with Long Short-Term Memory (LSTM) networks for time-series forecasting. Unlike prior studies, our approach systematically analyzes the trade-off between compression ratio and predictive accuracy, demonstrating how dimensionality reduction can improve both scalability and robustness. Thereby reducing the computational burden associated with processing massive-scale monitoring data. Experiments conducted on both synthetic and real-world datasets demonstrate that the proposed method achieves up to 60% data compression with minimal reconstruction loss, while also improving prediction accuracy compared to baseline LSTM models. We evaluate the overall performance of the framework using various metrics, including data reduction ratio, prediction accuracy, and the effects of different compression stages on predictive performance. Additionally, we quantify the computational savings in terms of CPU usage, memory footprint, and training/inference times, confirming the framework's feasibility for real-world deployment. These results underscore the potential of integrating compression and prediction to achieve scalable, accurate, and resource-efficient management of cloud workloads.