Question 14
In a class of $14$ boys and $17$ girls, some candies are to be distributed. Every boy receives an equal number of candies as each other, while every girl also receives an equal number of candies as each other. Each person receives at least one candy, but the number of candies received by each boy may be different from that received by each girl. If the total number of candies cannot be redistributed in any other way to satisfy our conditions, determine the maximum number of candies that we can have. Show your detailed solution.