Find the smallest integer \(N\) where \(N = \dfrac{A \text{ # } B}{B}\), where \(A\) and \(B\) are three-digit integers, and \((A \text{ # } B)\) denotes the six-digit integer formed by placing \(A\) and \(B\) side by side.

**Note**: Trivial solutions like \(\left[A=001, B=500, N=3 \right]\) are not allowed, so assume \(A, B \geq 100\).

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