<p>Neuronal synchrony is fundamental to healthy brain function, yet excessive synchronization can lead to neurological disorders such as epilepsy and Parkinson's disease. While the classical FitzHugh-Nagumo (FHN) model captures basic excitable dynamics, it lacks intrinsic memory properties that characterize real neurons. Recent memristive extensions address this limitation by incorporating history-dependent behaviour through adaptive circuit elements. Through comprehensive numerical simulations, we investigate how common multiplicative noise alone, as well as its interaction with diffusive coupling, produces synchronization in a pair of memristive FHN neurons. Our computational study examines three distinct scenarios: (i) synchronization driven solely by common multiplicative noise, (ii) synchronization through diffusive coupling alone, and (iii) combined effects of both mechanisms. We demonstrate that memristive neurons achieve robust phase synchronization with significantly reduced coupling requirements compared to classical FHN systems when subjected to shared stochastic inputs. Extensive parameter studies reveal a fundamental trade-off between coupling strength and noise intensity, where common multiplicative noise can effectively compensate for weak synaptic connections. Complementary heatmaps of Pearson correlation, synchronization time, and transverse Lyapunov exponents further delineate the parameter regimes supporting stable and efficient synchronization. These findings suggest novel therapeutic strategies for neurological disorders and provide design principles for next generation neuroprosthetics.</p>