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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) 1×2×3×⋯×6=(1×2×3)×(1×2×3×4×5)
Extending the above to a larger number, we find that there exists an integer N (>6)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), 1×2×3×⋯×N=(1×2×3×⋯×A)×(1×2×3×⋯×B), where AAA and BBB are both integers larger than 1.
What is the smallest N?N?N?
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