Why three-digit integers only?

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 \(A, B \geq 100\).


If you've solved this problem, try it's sister problem, an advanced version: Why three-digit integers only? (Part-2).
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