It's Only Divisible If You Add One

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

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

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