Workers A, B, and C take turns to be on duty according to different days. A is on duty every 6 days, B is on duty every 7 days, and C is on duty once every 8 days. After the three of them are on duty at the same time, at least how many days later will the three of them be on duty at the same time?
甲、乙、丙三个工人按不同天数轮流值班，甲6天值一次，乙7天值一次，丙8天值一次．他们三人同时值班后，至少再隔多少天后三个人再同时值班？
<gadget id="calculator">2 * 2 * 2 * 3 * 7</gadget>
<output>168</output>

<result>168</result>