factor each number into prime numbers:
note: the second 8 doesn't change anything. for example, the lcm of 8 and 8 is 8, the lcm of 8 and 8 and 8 is 8, and so on. repeating a number doesn't do anything
8 = 2 * 2 * 2
4 = 2 * 2
15 = 3 * 5
3 = 3
5 = 5
6 = 2 * 3
the lcm is 2 * 2 * 2 * 3 * 5 because 2 * 2 * 2 * 3 * 5 has 2 * 2 * 2 (to make 8), 2 * 2 (to make 4), 3 * 5 (to make 15), a 3 (to make 3), a 5 (to make 5), and 2 * 3 (to make 6).
2 * 2 * 2 * 3 * 5 = 120
the lcm of 8, 4, 15, 3, 5, 6, and 8 is 120