Henry Ernest Dudeney/Modern Puzzles/82 - Army Figures

by : $82$

 * Army Figures
 * A certain division in an army was composed of a little over twenty thousand men, made up of five brigades.
 * It was know that one third of the first brigade,
 * two-sevenths of the second brigade,
 * seven-twelfths of the third,
 * nine-thirteenths of the fourth,
 * ''and fifteen-twenty-seconds of the fifth brigades happened in every case to be the same number of men.
 * Can you discover how many men there were in every brigade?