Produce the least positive number that is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.

Because all numbers that are divisible by 10 is divisible by 5, all numbers that are divisible by 8 is divisible by 2 and 4, all numbers divisible by 6 is divisible by 2 and 3, we only need to find the smallest common multiple of 6,7,8,9,10 and 11

find the prime factors of each:

2,3

7

2,2,2,

3,3,

2,5,

11

factors that are shared can be used only once, so we have:

2*7*3*11*3*2*5*2=27720