6. Cesare owns a large number of toy soldiers, between 2000 and 2500. When he tries to arrange them in rows of 2, 3, 4, 5, 6, 7, there is always one left over. If he wants to arrange all of them in rows of the same length (greater than 1), what is the minimum length of such a row?
(A) 19
(B) 23
(C) 11
(D) 17
(E) 13
(6) The correct answer is $(C)$.

Indeed, if $n$ is the number of soldiers of Caesar, and there is always one left over when dividing by 2, 3, 4, 5, 6, and 7, it means that $n-1$ is divisible by all these numbers; therefore, $\operatorname{lcm}(2,3,4,5,6,7)=420$ divides $n-1$. The only multiple of 420 between 2000 and 2500 is 2100. Therefore, we have $n=2101$, whose smallest divisor (other than 1) is 11.

Question proposed by Matteo Rossi.