Let the number be N
1 = 1 so N must have factor 1 (every integer has factor 1, so we can ignore 1)
2 = 2 so N must have factor 2
3 = 3 so N must have factor 3
4 = 2*2 so N must have factor 2*2
5 = 5 so N must have factor 5
6 = 2*3 so N must have factor 2*3
7 = 7 so N must have factor 7
8 = 2*2*2 so N must have factor 2*2*2
9 = 3*3 so N must have factor 3*3
10 = 2*5 so N must have factor 2*5
So the smallest N can be and have at least as many of
every factor above is the product of three 2's, two 3's,
one 5, and one 7, which means
N = 2*2*2*3*3*5*7 = 2520
Edwin
