Find the smallest positive \(N\) such that \(\begin{align*} N &\equiv 6 \pmod{12}, \\ N &\equiv 6 \pmod{18}, \\ N &\equiv 6 \pmod{24}, \\ N &\equiv 6 \pmod{30}, \\ N &\equiv 6 \pmod{60}. \end{align*}\)
Since the LCM of [12, 18, 24, 30, 60] =360
Therefore the smallest positive N =360 + 6 = 366.
