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Posted: **Tue Sep 07, 2021 7:28 am**

: Is It True That If A And B Commute Then The Order Ab Of Ab Is The Least Common Multiple Of The Orders A B Of The El 1 (22.6 KiB) Viewed 52 times

Is it true that if a and b commute, then the order |ab| of ab is the least common multiple of the orders |a||b of the elements a, b? If it is true, prove it. If not true, please provide counter example.