The smallest positive number divisible by every integer from 2 to 10
You must find the least common multiple (LCM) of the positive integers 2 to 10
One way to find LCM's is to use prime factorization:
2 is prime
3 is prime
4 = 2 * 2 = 2 ^ 2
5 is prime
6 = 2 * 3
7 is prime
8 = 2 * 2 * 2 = 2 ^ 3
9 = 3 * 3 = 3 ^ 2
10 = 2 * 5
The LCM of all of these will be the product of all the different factors. When a factor appears in more than one list of factors, use the longest string of this factor. So:
LCM = 2 ^ 3 * 3 ^ 2 * 5 * 7 = 8 * 9 * 5 * 7 = 2520