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You could keep adding 51 to the right side until you get a multiple of 13: You would get 57, 108, 159, 210, 261, 312, and 312 is the first of these that is divisible by 13. This works, but is really too much work. Instead we could convert back to a Diophantine equation:

\begin{equation*} 13x = 6 + 51k\text{.} \end{equation*}

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