Find the smallest number that has the factors 1,2,3,4,5,6,7,8, 9
The smallest number that has the factors 1, 2, 3, 4, 5, 6, 7, 8, and 9 is the least common multiple (LCM) of those numbers.
To find the LCM, we can list out the prime factorizations of each number:
1: 1
2: 2
3: 3
4: 2^2
5: 5
6: 2 * 3
7: 7
8: 2^3
9: 3^2
To find the LCM, we need to consider the highest power of each prime factor that appears in any of the factorizations:
1: 1
2: 2^3
3: 3^2
4: 2^2
5: 5
6: 2 * 3
7: 7
8: 2^3
9: 3^2
Now, we need to multiply these prime factors together:
1 * 2^3 * 3^2 * 5 * 7 = 2 * 8 * 9 * 5 * 7 = 10080
Therefore, the smallest number that has the factors 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 10,080.