15a^3b^4, 42a^2b^5c (find LCM)

Question

find the LCM (least common multiple) of each of the follo.wing, 15a^3b^4, 42a^2b^5c (^ meaning "to the power of")

Answer 1

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