We play a version of this in Korea called "Sam-Yuk-Gu" (3-6-9). Same thing going around in a circle, except they have to clap on any number containing a 3, 6, or a 9 (not multiples of 3 though - you wouldn't clap on 12 for example). You can then "upgrade" the game by adding another "catch" - they have to say "OK!" or whatever on multiples of 5. I also use this game to review ordinal numbers (first, second, third...).
When I look at the smiles on all the children's faces, I just know they're about to jab me with something - Homer Simpson