gum (n.1) Look up gum at Dictionary.com
"resin," c.1300, from Old French gome "(medicinal) gum, resin," from Late Latin gumma, from Latin gummi, from Greek kommi "gum," from Egyptian kemai. As a shortened form of chewing gum, first attested 1842 in American English. The gum tree (1670s) was so called for the resin it exudes.
gum (n.2) Look up gum at Dictionary.com
"membranes of the mouth," Old English goma "palate, side of the mouth" (single or plural), from a Germanic source represented by Old Norse gomi "palate," Old High German goumo; related to Lithuanian gomurys "palate," and perhaps from PIE *gheu- "to yawn" (source also of Greek khaos; see chaos).
gum (v.) Look up gum at Dictionary.com
early 14c., gommen, "treat with (medicinal or aromatic) gums," from gum (n.1). In the transferred or figurative sense of "spoil, ruin" (usually with up), it is first recorded 1901, probably from the notion of machinery becoming clogged. Of infants, etc., "to chew or gnaw (something) with the gums," by 1907, from gum (n.2). Related: Gummed; gumming.