\[\boxed{\text{670\ (670).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[НОК\ (1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7) =\]
\[= 2 \cdot 3 \cdot 2 \cdot 5 \cdot 7 = 420\]
\[1 = 1,\ \ 2 = 2 \cdot 1,\ \ \]
\[3 = 3 \cdot 1,\ \ 4 = 2 \cdot 2\]
\[5 = 5 \cdot 1,\ \ 6 = 2 \cdot 3,\]
\[\ \ 7 = 7 \cdot 1\]
\[Ответ:420\ дней.\]