We present Local LoRA, a memory-flexible fine-tuning approach that, in principle, can fine-tune an arbitrarily large model on fixed hardware, including consumer grade GPUs. Our approach aims to decouple the size of the model and the memory required to fine-tune it by dividing the model into chunks and sequentially fine tuning each chunk. Our results show that Local LoRA closes the gap between the un-tuned model and end-to-end LoRA on math reasoning tasks.