first, the numbers:
the lcm of 15 and 42 is
15 = 3 * 5
42 = 2 * 3 * 7
we want a 2
we want one 3 (because they both have it already, we don't need two 3's)
we want a 5 and a 7
2 * 3 * 5 * 7 = 210
the lcm of 15 and 42 is 210
now the a's
the lcm of a^3 and a^2 is a^3
note: a^3 = a^2 * a
now the b's
the lcm of b^4 and b^5 is b^5
now the c's
the lcm of 1 and c is c
note: since 15(a^3)(b^4) doesn't have a c, it's like there's a *1 sitting there
the lcm of the whole thing is 210(a^3)(b^5)c