Today we learned about subgroups of cyclic groups G = <a>. During the discussion we reached this point: |<a^k>| = minimum L, L > 0, such that a^(kL) = 1. |G| = n. Then a^kL = a^bn, thus kL = bn, and thus L = n/gcd(k, n). However, I don't understand the bolded. My number theory is terrible, and I don't really see where the gcd(k, n) comes from. I understand that if gcd(k, n) = 1 that <a^k> = <a>, but the connection to L = n/gcd(k,n) just isn't apparent to me. Can someone shine some light on this for me? Thanks, I appreciate it!