Required Mathematical Intelligence

Chapter 60 Seven Friends
Someone has seven friends.The first friend visits him at his house every night, the second friend visits his house every other night, the third friend visits his house every two nights, and the fourth friend visits him every three nights His family is a guest.And so on until the seventh friend shows up at his house every six nights.

Do the seven friends often meet at the host's house on the same evening?
[答案：毫无疑问，这七位朋友经过若干天以后，有一个晚上在主人家里碰面。这一天追溯到第一位朋友开始访问的那个晚上，所经历的天数，一定能被2、3、4、5、6、7各数整除；换而言之，第一天与七个朋友碰面那一天，中间相隔的天数，应该是2、3、4、5、6、7各数的最小公倍数。不难求出这个数为420.每隔420天这七位朋友就将在主人家里碰面一次。]
(End of this chapter)