It's Only Divisible If You Add One

All of the following statements are true, except one. Which one?

(1) 1×2(1) \ \, 1\times 2 is not divisible by 3.
(2) 1×2×3(2) \ \, 1\times 2\times 3 is not divisible by 4.
(3) 1×2×3×4(3) \ \, 1\times 2\times 3\times 4 is not divisible by 5.
(4) 1×2×3×4×5(4) \ \, 1\times 2\times 3\times 4\times 5 is not divisible by 6.

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