Unsimplifying a Fraction

Find the smallest positive integer \(N \neq 23\) such that the fraction \( \frac {N-23} { 7N+6 } \) is not in simplest terms.

Details and assumptions

A fraction \(\frac{a}{b}\) is in simplest terms if \(a\) and \(b\) are coprime integers.

As a specific example, the fraction \( \frac {6}{4} \) is not in simplest terms since \( \gcd(4, 6) = 2 \neq 1\). It can be simplified to \( \frac {3}{2} \).

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