Hallucinations in large language models (LLMs), defined as fluent yet incorrect or incoherent outputs, pose a significant challenge to the automatic generation of educational multiple-choice questions (MCQs). We identified four key hallucination types in MCQ generation: reasoning inconsistencies, insolvability, factual errors, and mathematical errors. To address this, we propose a hallucination-free multi-agent generation framework that breaks down MCQ generation into discrete, verifiable stages. Our framework utilizes both rule-based and LLM-based detection agents, as well as hallucination scoring metrics to optimize question quality. We redefined MCQ generation as an optimization task minimizing hallucination risk while maximizing validity, answerability, and cost-efficiency. We also introduce an agent-led refinement process that uses counterfactual reasoning and chain-of-thought (CoT) to iteratively improve hallucination in question generation. We evaluated a sample of AP- aligned STEM questions, where our system reduced hallucination rates by over 90% compared to baseline generation while preserving the educational value and style of questions. Our results demonstrate that structured multi-agent collaboration can mitigate hallucinations in educational content creation at scale, paving the way for more reliable LLM-powered learning tools.