59(982). In the cabinet, there are books that need to be packed. If they are bundled in groups of 4, 5, or 6, there will always be one extra book left each time, but if they are bundled in groups of 7, there will be no extra books left. What is the number of books in the cabinet, given that there are no more than 400 books?
Solution. The problem reduces to finding a natural number that is a multiple of seven, not exceeding 400, which gives a remainder of 1 when divided by 4, 5, and 6. This number, obviously, has the form $60 n+1$, where 60 is the least common multiple of the numbers $4,5,6, n \in \boldsymbol{N}$, $n<7$. By trial, we find $n=5$. Answer: 301.

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