Turing’s chain will fall off when his bicycle reaches the state ([theta] = 0, C = 0) and in light of what is written above, this will happen when i (which is just a counter telling how many times the rear wheel has revolved) reaches some hypothetical value such that in mod l = 0, or, to put it in plain language, it will happen if there is some multiple of n (such as, oh, 2 n , 3 n , 395 n or 109,948,368,443 n ) that just happens to be an exact multiple of l too. Actually there might be several of these so-called common multiples, but from a practical standpoint the only one that matters is the first one—the least common multiple, or LCM—because that’s the one that will be reached first and that will cause the chain to fall off.