first, the numbers
the lcm of 21, 7, and 15
21 = 3 * 7
7 = 7
15 = 3 * 5
for an lcm you times together a set of numbers that includes enough numbers to make each of those factors (???) like this:
to make 21 you need a 3 and a 7
to make 7 you just need 7
to make 15 you need a 3 and a 5
to make the lcm, you want 3 * 5 * 7 because 3 * 5 * 7 has a 3 * 7 (to make 21), a 7 (to make 7), and a 3 * 5 (to make 15).
the lcm of 21, 7, and 15 is 3 * 5 * 7 = 105
now the c's
the lcm of c^3, c^2, and c^5 is c^5
now the b's
the lcm of b^8, b^3, and b^7 is b^8
the lcm of the whole thing is 105(c^5)(b^8)