before vowels mult-, word-forming element meaning "many, many times, much," from combining form of Latin multus "much, many," from PIE *ml-to-, from root *mel- (2) "strong, great, numerous." It was much-used in forming Latin compounds in classical times and after (such as multianimis "having much courage," multibibus "much-drinking," multicomus "having much hair," multiloquus "talkative"). Many English words that use it (multinational, etc.) are 20c. coinages.
late 14c., "one who or that lays" (especially stones, "a mason"), agent noun from lay (v.). Passive sense of "a thickness of some material laid over a surface" is first recorded 1610s, but because the earliest English use was in cookery this is perhaps from French liue "binding," used of a thickened sauce. Of hens from 1707. Layer cake attested from 1875.
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Harper, D. (n.d.). Etymology of multilayer. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/multilayer