This research introduces a novel approach to textual and multimodal Hate Speech Detection (HSD), using Large Language Models (LLMs) as dynamic knowledge bases to generate background context and incorporate it into the input of HSD classifiers. Two context generation strategies are examined: one focused on named entities and the other on full-text prompting. Four methods of incorporating context into the classifier input are compared: text concatenation, embedding concatenation, a hierarchical transformer-based fusion, and LLM-driven text enhancement. Experiments are conducted on the textual Latent Hatred dataset of implicit hate speech and applied in a multimodal setting on the MAMI dataset of misogynous memes. Results suggest that both the contextual information and the method by which it is incorporated are key, with gains of up to 3 and 6 F1 points on textual and multimodal setups respectively, from a zero-context baseline to the highest-performing system, based on embedding concatenation.