Find the smallest positve $n$ 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*}
+981 Hey Guest!
\(\begin{align*} N &\equiv 6 \pmod{12}, \\ N &\equiv 6 \pmod{18}, \\ N &\equiv 6 \pmod{24}, \\ N &\equiv 6 \pmod{30}, \\ N &\equiv 6 \pmod{60}. \end{align*}\)
LCM [12, 18, 24, 30, 60] = 360
N = 360k + 6.
6 is your answer.
Guest is right, my previous answer was wrong.
I hope this helped,
gavin
