Large language models (LLMs) have achieved remarkable success across diverse tasks through large-scale pretraining. However, they remain prone to catastrophic forgetting in continual learning. To the best of our knowledge, this is the first work to identify noise accumulation in LoRA updates as a key cause of forgetting in continual learning. A preliminary two-task experiment demonstrates that removing less important components of the second task’s LoRA parameters improves performance on the first task, suggesting that later updates introduce noisy interference. Building on this insight, we propose **S**ubspace-Denoised **Lo**w-**R**ank **A**daptation (**SLoRA**), a simple and effective framework that filters noisy components from LoRA updates via subspace similarity with the base model. SLoRA is a regularization-free method without accessing data or gradients from previous tasks or modifying the training process. It offers two variants, SLoRA-Pre and SLoRA-Post, for online and offline continual learning, respectively. Extensive experiments across tasks and models validate the effectiveness of SLoRA. It improves final accuracy by up to 12%, reduces forgetting by 29%, and filters out over 30% of LoRA parameters identified as noisy. Our code is available at https://github.com/alina1031/SLoRA.