find the least common multiple

Question

find the least common multiple for -2, (x + 2)², x² - 4.

Answer 1

-2

(x+2)(x+2)

(x-2)(x+2)

are the fully factored quantities of which you seek the LCM.

 

Think of it this way: Do a survey and build up an expression containing enough factors so that each of the above three expressions are a subset.  Or, in other words, The first listed quantity contributes -2 to the LCM, the second listed quantity contributes (x+2)(x+2), two identical factors; the third listed quantity contributes a new factor (x-2) but we already have enough (x+2)'s to satisfy the demands made by the third listed quantity.

 

Thus, LCM = -2(x+2)(x+2)(x-2) and you see that all demands made by any of the three listed quantities are satisfied.