$1\times2\times3\times\cdots \times6 = (1\times2\times3)\times(1\times2\times3\times4\times5)$

Extending the above to a larger number, we find that there exists an integer $N\, (>6)$ such that $1\times2\times3\times\cdots \times N = (1\times2\times3\times \cdots \times A)\times(1\times2\times3\times\cdots\times B),$ where $A$ and $B$ are both integers larger than 1.

What is the smallest $N?$

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