Shortcut to Least Common Multiple

Is there a shorter way to find the LCM of 4 numbers besides just listing them out?

For instance, the LCM of 6, 7, 8, and 9. (this was a question in the data analysis fundamentals quiz and greg said you could forget about the 6 - why?)

\operatorname{lcm}(6,7,8,9) = \operatorname{lcm} (6, \operatorname{lcm}(7,8,9)) = \operatorname{lcm} (6, 504) = 504

Maybe something like that?