Update: The suggested tag synonyms lcm ⇒ divisibility and least-common-multiple ⇒ divisibility have been withdrawn. See my answer here for related goings-on.
EDIT3: There is now a separate post discussing these tags: http://meta.math.stackexchange.com/questions/20664/on-gcd-and-greatest-common-divisor-and-other-similar-tags
So if these tags are discussed further, it should be done there.
The tag gcd is already synonym of divisibility.
It seems logical that the tag least-common-multiple should also be a synonym. (And maybe also lcm could be created and added to the synonyms; so that some user does not create this tag as a separate tag in the future.) As I do not have sufficiently high score in divisbility to suggest a synonym, I am posting this suggestion here.
The recent revisions of (least-common-multiple) tag-excerpt and tag-wiki specifically mention that the notion of lcm exists not only for integers but also in rings. (And that the tag is also suitable for this usage.) I don't think this should cause a problem, since rings are also mentioned in the tag-wiki for divisibility. (Although it not explicitly mentioned at the current version of tag-excerpt.) Note that the tag-wiki for divisibility explicitly mentions both gcd and lcm.
EDIT: quid added this to the suggested synonyms. So it is now possible to vote on these synonyms here.
EDIT2: The gcd tag was made a synonym of divisibility as a result of this discussion: http://meta.math.stackexchange.com/questions/10998/on-the-gcd-tag.
In this post I merely suggested that lcm should be treated similarly as gcd.
If (gcd) being synonym of (divisibility) seems problematic to some users (as the comments suggests), it should be probably discussed in a separate thread. (I am not sure what happens to the questions tagged by the synonymous tags if a tag-synonym is removed from the system. And a synonym definitely should not be removed without discussing such step first.)
