3. Some integers, when divided by $\frac{5}{7}, \frac{7}{9}, \frac{9}{11}, \frac{11}{13}$ respectively, yield quotients that, when expressed as mixed numbers, have fractional parts of $\frac{2}{5}, \frac{2}{7}, \frac{2}{9}, \frac{2}{11}$ respectively. The smallest integer greater than 1 that satisfies these conditions is $\qquad$ .
Let the integer be $A$, when divided by $\frac{5}{7}, \frac{7}{9}, \frac{9}{11}, \frac{11}{13}$ respectively, the quotients are $\frac{7}{5} A, \frac{9}{7} A, \frac{11}{9} A, \frac{13}{11} A$;
$$
\frac{7}{5} A=1+\frac{2}{5}+\frac{7}{5}(A-1), \frac{9}{7} A=1+\frac{2}{7}+\frac{9}{7}(A-1), \frac{11}{9} A=1+\frac{2}{9}+\frac{11}{9}(A-1), \frac{13}{11} A=1+\frac{2}{11}+\frac{13}{11}(A-1)
$$

Obviously, when $A-1$ is $[5,7,9,3]$, it satisfies the condition. Therefore, $A-1=3465, A=3466$.