Although recent end-to-end video generation models demonstrate impressive performance in visually oriented content creation, they remain limited in scenarios that require strict logical rigor and precise knowledge representation, such as instructional and educational media. To address this problem, we propose LASEV, a hierarchical LLM-based multi-agent system for generating high-quality instructional videos from educational problems. LASEV formulates educational video generation as a multi-objective task that simultaneously demands correct step-by-step reasoning, pedagogically coherent narration, semantically faithful visual demonstrations, and precise audio--visual alignment. To address the limitations of prior approaches--including low procedural fidelity, high production cost, and limited controllability--LASEV decomposes the generation workflow into specialized agents that collaborate through a central Orchestrating Agent, shared production state, explicit quality gates, and iterative critique mechanisms. Specifically, the Orchestrating Agent supervises a Solution Agent for rigorous problem solving, an Illustration Agent that produces executable visualization code, and a Narration Agent for learner-oriented instructional scripts. In addition, all outputs from the working agents are subject to semantic critique, rule-based constraints, and tool-based compilation checks. Rather than directly synthesizing pixels, the system constructs a structured executable video script that is deterministically compiled into synchronized visuals and narration using template-driven assembly rules, enabling fully automated production without manual editing. In large-scale deployments, LASEV achieves a throughput exceeding one million videos per day, delivering over a 95% reduction in cost compared to current industry-standard approaches while maintaining a high acceptance rate.