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We conducted local anodic oxidation (LAO) lithography in single-layer, bilayer, and multilayer graphenes using tapping-mode atomic force microscope. The width of insulating oxidized area depends systematically on the number of graphene layers. An 800-nm-wide bar-shaped device fabricated in single-layer graphene exhibits the half-integer quantum Hall effect. We also fabricated a 55-nm-wide graphene nanoribbon (GNR). The conductance of the GNR at the charge neutrality point was suppressed at low temperature, which suggests the opening of an energy gap due to lateral confinement of charge carriers. These results show that LAO lithography is an effective technique for the fabrication of graphene nanodevices.