What’s the LCM of this question

Question

10(x+3)³(x-2)² and 12(x+3)²(x-2)

Answer 1

10 (x + 3)³(x - 2)² = 2 * 5 * (x + 3)³ * (x - 2)²

12 (x + 3)²(x - 2) = 2² * 3 * (x + 3)² * (x - 2)

LCM = 2² * 3 * 5 * (x + 3)³ * (x - 2)² = 60(x + 3)³(x - 2)² ----- ANSWER

Answer 2

Joseph,

David has done the hard part, by identifying the factors and multiplicities of each factor for both expressions:

2(5)(x + 3)(x + 3)((x + 3)(x - 2)(x - 2)

and...

2(2)(3)(x + 3)(x + 3)(x - 2)

2

To find the Least Common Multiple, you need to use the larger of each multiplicity for each factor. If we’ll call the two expressions A and B,

A has factors 2, 5, (x+3)³, (x-2)²

B has factors 2², 3, (x+3)², (x-2)

the LCM has to have the larger of each power, such as 2².

so the answer is

2²,3, 5, (x+3)³, (x-2)², all multiplied together.

Answer 3

Well, you have...

2(5)(x + 3)(x + 3)((x + 3)(x - 2)(x - 2)

and...

2(2)(3)(x + 3)(x + 3)(x - 2)

What do both have in common?

2(x + 3)(x + 3)(x - 2) = 2(x + 3)²(x - 2)