This paper proposes a targetless and automatic camera-LiDAR calibration method. Our approach extends the hand-eye calibration framework to 2D-3D calibration. The scaled camera motions are accurately calculated using a sensor fusion odometry method. We also clarify the suitable motions for our calibration method. Whereas other calibrations require the LiDAR reflectance data and an initial extrinsic parameter, the proposed method requires only the three-dimensional point cloud and the camera image. The effectiveness of the method is demonstrated in experiments using several sensor configurations in indoor and outdoor scenes. Our method achieved higher accuracy than comparable state-of-the-art methods.