Need help

Melody:

The smallest N is 6. The LCM of[12, 18, 24, 30, 60] = 360. Therefore:

N = 360k + 6, where k = 0, 1, 2, 3.........etc.

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

The smallest N is 6, the rest of my answer was incorrect.