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Find the smallest positive \(N\) such that​ \(\begin{align*} N &\equiv 6 \pmod{12}, \\ N &\equiv 6 \pmod{18}, \\ N &\equiv 6 \pmod{24}, \\ N &\equiv 6 \pmod{30}, \\ N &\equiv 6 \pmod{60}. \end{align*}\)

 Dec 21, 2018
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Since the LCM of [12, 18, 24, 30, 60] =360

Therefore the smallest positive N =360 + 6 = 366.

 Dec 21, 2018

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