The Limit Comparison Test is a method used in calculus to determine the convergence or divergence of infinite series. It compares a given series with a known benchmark series. If the limit of the ratio of the two series approaches a positive finite number, both series will either converge or diverge together. To apply the test, consider two series: the series of interest, say Σa_n, and a known series, Σb_n. Calculate the limit of a_n/b_n as n approaches infinity. If this limit is a positive finite number, then both series share the same convergence behavior.