From Middle English laughen, laghen, from (Anglian) Old English hlæhhan, hlehhan, (West Saxon) hliehhan, from Proto-West Germanic *hlahhjan, from Proto-Germanic *hlahjaną.
Germanic: (with j-present) Scots lauch, Icelandic hlæja, Norwegian, Swedish and Danish le; (without) Low German lachen, Dutch lachen, German lachen.