Le Conte Mountain sits high above the south end of the Yang Yang Lakes in the middle of Washington State's Ptarmigan Traverse. According the the 1st Edition of the Beckey guide book:
The mountain is a 2-mi.-long NW trending ridge, the center of intense alpine glaciation, scoured by both the Le Conte and South Cascade glaciers. There are a rugged and prominent S Summit (7612'), and a middle summit (7456'). The mountain is named for the Sierra Nevada geologist Joseph Le Conte
The main summit of the mountain offers outstanding views of the surrounding areas as there is at least 500' of near-vertical relief on both the south and north faces. For those on the N-to-S Ptarmigan Traverse it offers the first clear view of the large South Cascade valley-glacier.
The main page for the Ptarmigan Traverse has an excellent description for getting to the Yang Yang Lakes (and to Le Conte). As an additional note:
From the lakes, go south and around the forested ridge protruding down from the western skyline. Ascended trail/talus up the ridge (there is a higher camp on this ridge if the bugs/people at Yang Yang Lakes are a problem) until the ridge rises up sharply and drops off on the right (North) side. We ascended a precipitous path up compacted dirt and rock through a small gully which led to a 15-20 foot wide grassy ledge. Walk along the grassy ledge (west) and make a 180 degree turn at its far end to gain a nice path up to the top of the ridge. We affectionately called this the "secret stair".
Follow this along the ridge line until you gain a rock outcropping immediately under the North Face of Le Conte Mountain. Ditch the packs here and proceed.
See the main PT page for information.