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In an answer to my question here Relationship between order of $(x,y)$ in $G \times G'$ and order of disjoint permutations, which both involve LCMs?, it is said that

Let $G$ be a group, $a\in G$ of order $r$ and $b\in G$ of order $s$.

If $ab=ba$, then the order of $ab$ is $\operatorname{lcm}(a,b)$.

I submitted an edit to change this to $\operatorname{lcm}(r,s)$, but I was denied. Here is the denial: https://math.stackexchange.com/review/suggested-edits/1085060 Later this was edited by José Carlos Santos into the current revision. Here is the edit into the current revision: https://math.stackexchange.com/revisions/2954951/2

The one who is answered is Scientifica. I asked him/her what $\operatorname{lcm}(a,b)$. The reply was

@JackBauer It means "the least common multiple of a and b". You used it yourself in your question ;)

  1. What is the definition of the least common multiple of elements of a group? I could not find this online. I thought LCM was for integers under the addition operation and under the usual topology on $\mathbb Z$ (and under the usual everything in every branch of mathematics).

  2. Where did I use the concept of least common multiple of elements of a group in my question?

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    $\begingroup$ Scientifica has now clarified that your suggested edit was correct (the rejection must have been a mistake). There is no such thing as least common multiple in a group. $\endgroup$ – Arnaud D. Oct 14 '18 at 12:28
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There's no such thing as least common multiple in a group. Every element of a group is a multiple of every other element.

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