late 14c., dragme, "ancient Athenian coin," the principal silver coin of ancient Greece; mid-15c. as the name of a coin used in Syria, from Old French dragme, from Medieval Latin dragma, from Latinized form of Greek drakhme, an Attic coin and weight, probably originally "a handful" (of six obols, the least valuable coins in ancient Athens), akin to drassesthai "to grasp," a word of uncertain origin, perhaps Pre-Greek. Arabic dirham, Armenian dram are from Greek.
Middle English also used the word in the "weight" sense, as a unit of apothecary's weight of one-eighth of an ounce, which became dram.