Large-language models (LLMs) are rapidly being applied to radiology, enabling automated image interpretation and report generation tasks. Their deployment in clinical practice requires both high diagnostic accuracy and low inference latency, which in turn demands powerful hardware. High-performance graphical processing units (GPUs) provide the necessary compute and memory throughput to run large LLMs on imaging data. We review modern GPU architectures (e.g. NVIDIA A100/H100, AMD Instinct MI250X/MI300) and key performance metrics of floating-point throughput, memory bandwidth, VRAM capacity. We show how these hardware capabilities affect radiology tasks: for example, generating reports or detecting findings on CheXpert and MIMIC-CXR images is computationally intensive and benefits from GPU parallelism and tensor-core acceleration. Empirical studies indicate that using appropriate GPU resources can reduce inference time and improve throughput. We discuss practical challenges including privacy, deployment, cost, power and optimization strategies: mixed-precision, quantization, compression, and multi-GPU scaling. Finally, we anticipate that next-generation features (8-bit tensor cores, enhanced interconnect) will further enable on-premise and federated radiology AI. Advancing GPU infrastructure is essential for safe, efficient LLM-based radiology diagnostics.