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*}

Guest May 11, 2018

#1**+1 **

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

GYanggg
May 11, 2018