A quiz-master wants to buy a box of chocolates that can be shared out equally, with none left over, among any group of children numbering from 2 up to 12.
What is the smallest number of chocolates the box can hold?

The number must be a common multiple of 2, 3, 4, ..., 12, so the smallest is their LCM. Taking the highest power of each prime up to 12 gives $2^3\times 3^2\times 5\times 7\times$ 11 = 27720. Answering 2520 is the LCM of 2 to 10 only and misses the factor 11; 55440 is twice as large as needed; 13860 is half of 27720 and is not divisible by 8.