# 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 $$A, B \geq 100$$.

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