Abstract: A lathe capable of performing both usual machining and balance correction machining of a workpiece. In a combined machining lathe having a drilling and/or milling machine, vibration sensor(s) are attached to a headstock and/or a tailstock and a sensor for detecting a rotation angle of a main spindle is provided. After the usual machining, the workpiece is rotated at a predetermined rotating speed on the same lathe and an amount of imbalance and phase are calculated by a imbalance arithmetic unit. An NC machining program for balancing the workpiece is automatically produced by a balance correction machining program producer within a numerical controller and balance correction machining of the workpiece is carried out using a rotary tool such as a drill or the like.