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We implemented a compact, robust, and stable device for simultaneous frequency stabilization of lasers with different wavelengths used for the cooling and trapping of Yb atoms in an optical lattice clock. The lasers at 399, 556, and 759 nm are locked to a single ultra-stable cavity using the offset sideband locking technique, a modified version of the Pound-Drever-Hall method. For the most demanding stabilization here, the 556 nm laser, this system exhibits a 300 Hz linewidth for an integration time of 80 ms. We observed a long-term drift of less than 20 kHz per day at 759 nm that is suitable for operating the lattice laser with a light shift uncertainty below 1×10 -18 . We successfully tested the system for operating the clock during a typical working day by simultaneously locking the three lasers to the cavity.