Unsimplifying a Fraction

Find the smallest positive integer N23N \neq 23 such that the fraction N237N+6 \frac {N-23} { 7N+6 } is not in simplest terms.

Details and assumptions

A fraction ab\frac{a}{b} is in simplest terms if aa and bb are coprime integers.

As a specific example, the fraction 64 \frac {6}{4} is not in simplest terms since gcd(4,6)=21 \gcd(4, 6) = 2 \neq 1. It can be simplified to 32 \frac {3}{2} .

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