If you want the official "book procedure" to remove and replace the rear tire you will find it here This procedure requires unhooking electrical connections, removing the seats, rear fender and a few other things such as muffler brackets etc. All-in-all the book procedure looks pretty tedious so I didn't follow it.

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Before I tell you my method here is the standard warning. You are going to remove the rear wheel, your LC is heavy, if your LC is not secured on a suitable lift it may fall over. If it falls over it will get messed up. If it falls over on you, you will get messed up. Make sure you have it securely raised and restrained before removing the wheels. If you have any question if you can safely accomplish any part of this explanation, take your bike to an authorized service center and have it done. In other words if you hurt your LC, or yourself or both... not my problem, you been warned.

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Before you set about raising the bike you need to remove the rear axle covers and loosen, but do not remove the axle nut. The axle nut on my LC was extremely tight and required a little special attention with a large wrench and a rubber mallet. Your factory tool kit has a socketed wrench designed to fit the nut.

Next loosen the forward bolt of the rear caliper mounting bracket. If you click the image you will get a larger image with arrows pointing specifically to which one I am talking about. You may need to also bend the brakeline holding clamp to allow some slack in the brake line.