mid-12c., multeplien, "to cause to become many, cause to increase in number or quantity," from Old French multiplier, mouteplier (12c.) "increase, get bigger; flourish; breed; extend, enrich," from Latin multiplicare "to increase," from multiplex (genitive multiplicis) "having many folds, many times as great in number," from combining form of multus"much, many" (see multi-) + -plex "-fold," from PIE root *plek- "to plait."
Intransitive sense of "grow or increase in number or extent" (especially "to have children, produce offspring") is from mid-14c. Mathematical sense "perform the process of multiplication" is attested from late 14c. Related: Multiplied; multiplying.