ABSTRACTIntrinsic and extraneous cognitive loads compete for limited cognitive resources during reasoning tasks, potentially impairing reasoning performance. It is still unclear how these two cognitive loads interact to influence inductive reasoning. In this study, the event‐related potentials (ERPs) technique was used to investigate how numerical inductive reasoning was affected by intrinsic and extraneous cognitive loads, which were manipulated through relational complexity (simple vs. hierarchical rules) and the dot memory task (low vs. high executive load), respectively. Participants were required to identify hidden rules from three‐digit sequences and judge whether a probe was congruent with the rules. Behavioral results showed that reasoning performance on probes was affected by intrinsic and extraneous cognitive loads independently. The ERP results locked to the third numbers further revealed that intrinsic cognitive load modulated the N200, LPC, and LNC components, which reflected pattern detection, working memory updating, and relational integration processes, respectively. However, extraneous cognitive load enhanced P200 amplitudes, indicating attentional allocation to task‐irrelevant stimuli. Most importantly, the interaction between intrinsic and extraneous cognitive loads on N400 suggested that semantic integration resources competed when processing hierarchical rules under high extraneous cognitive load. Our findings provide psychophysiological evidence that intrinsic and extraneous cognitive loads affect numerical inductive reasoning through distinct yet interacting neural mechanisms, advancing our understanding of cognitive load theory with implications for educational practices.