What you would do is find the multiples of each number first (besides 0). For 600, there is 600, 1200, 1800, 2400, 3000, 3600, 4000, etc.
And for 108: 108, 216, 324, 432, 540, 648, etc.
The lowest number that is included in both sets would be 5,400, therefore that is the LCM.