First we want the least common multiple (LCM) of 8, 10, and 12. Write out their factors like this:
8 = 2 * 2 * 2
10 = 2 * 5
12 = 2 * 2 * 3
It's like we're making a parts list with enough parts to make 8, 10, or 12. In this case the list is 2 * 2 * 2 * 3 * 5 because that list has enough parts to make 8, 10, or 12.
2 * 2 * 2 * 3 *5 = 120
120 is the LCM of 8, 10, and 12.
Now we want the biggest 3 digit number that 120 can fit into evenly.
999 / 120 = 8.325
But we want whole numbers, so let's take just the 8 and do this:
8 * 120 = 960
Answer: 960 is the greatest 3 digit number exactly divisible by 8, 10, and 12.