The Great Divide

The key to solving this problem is finding all of the numbers prime factors and how many of each make up the number. We can write the numbers 2-9 like this (We are discluding the number 1 since the number 1 has no prime factors):

• 2 = 2
• 3 = 3
• 4 = 2 * 2
• 5 = 5
• 6 = 2 * 3
• 7 = 7
• 8 = 2 * 2 * 2
• 9 = 3 * 3

If we were to multiply the numbers 2-9 together, we need to make sure we do not have any of the above products repeated while we are solving this problem, which is why we can't just simply multiply the number 2-9 together.

Because of the products we've written above, we already know:

• if a number is divisible by 9, it is definitely divisible by 3,
• if it is divisible by 8, it is divisible by 2 & 4,
• if it is divisible by 9 & 8, it will be divisible by 6, since 2 * 3 = 6.

Therefore, we don't need to multiply the numbers 2, 3, 4, or 6 to get our solution.

5 * 7 * 8 * 9 = $\boxed{2520}$

Take LCM of 2,3,4, 5,6,7,8 & 9 or multiply 5,7,8, & 9
it is 2520

This problem becomes easier when we note that

$\displaystyle \begin{aligned} \text{lcm}(2, 4, 8) & = 2^3 \\ \text{lcm}(3, 9) & = 3^2 \\ \text{lcm}(5) & = 5^1 \\ \text{lcm}(7) & = 7^1 \\ 6 & = 2 \times 3 \end{aligned}$

Thus, $\text{lcm}(1, 2, 3, 4, 5, 6, 7, 8, 9) = 2^3 \times 3^2 \times 5 \times 7 = \boxed{2520}$