A modular LED unit having a number of LED modules separately mounted on individual interconnected preferably-extruded heat sinks, each heat sink having: a base configured to engage and hold an LED module in place and, in preferred forms, to facilitate the ganging of heat-sink/LED modules; and a plurality of fins, including inner-fins and side-fins, projecting from the opposite surface of the base and extending therealong, the side-fins having interlocking features to facilitate the ganging of heat-sink/module units together and, in preferred forms, to facilitate interconnection of the modular LED unit to other portions of a lighting fixture.