Factorial, factorial, factorial

Algebra Level 2

1×2×3××6=(1×2×3)×(1×2×3×4×5) 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)N\, (>6) such that 1×2×3××N=(1×2×3××A)×(1×2×3××B), 1\times2\times3\times\cdots \times N = (1\times2\times3\times \cdots \times A)\times(1\times2\times3\times\cdots\times B), where AA and BB are both integers larger than 1.

What is the smallest N?N?

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