You can express $8, 9, 6, 4, 2, 5$ and $7$ as $2^3, 3^2, 2 \times 3, 2^2, 2, 5$ and $7$.
That means the LCM must contain $2^3, 3^2, 5$ and $7$ to ensure that it is a multiple of all the numbers.
So the LCM is $2^3 \times 3^2 \times 5 \times 7 = 2520$.