factor each number into prime numbers like this
7 = 7
8 = 2 * 2 * 2
10 = 2 * 5
the lcm is 2 * 2 * 2 * 5 * 7 because 2 * 2 * 2 * 5 * 7 has a 7 (to make 7), a 2 * 2 * 2 (to make 8), and a 2 * 5 (to make 10).
2 * 2 * 2 * 5 * 7 = 280
the lcm of 7, 8, and 10 is 280