In Digital Logic Design (DLD), common logic gate IC numbers belong to the 7400-series, with key examples being 7408 for AND, 7432 for OR, 7400 for NAND, 7402 for NOR, and 7404 for NOT (Inverter), while 7486 is for XOR, all offering multiple gates per chip (e.g., quad 2-input) for building digital circuits and verifying truth tables.