Question

Find the least common multiple of x2 – 8x + 12 and x2 – x – 2.

Answer 1

Answer with Step-by-step explanation:

We have to find the least common multiple of x² – 8x + 12 and x² – x – 2.

on factoring both the terms separately:

x² – 8x + 12

=x²-6x-2x+12

=x(x-6)-2(x-6)

= (x-2)(x-6)

x² – x – 2

=x²-2x+x-2

=x(x-2)+1(x-2)

= (x-2)(x+1)

The factor (x-2) is common between them so we take it once

∴ LCM = (x-2)(x-6)(x+1)

Hence, least common multiple of x² – 8x + 12 and x² – x – 2 is:

(x-2)(x-6)(x+1)

Answer 2

The least common multiple of x² – 8x + 12 and x² – x – 2.

by factoring:
∴ x² – 8x + 12 = (x-2)(x-6)

x² – x – 2 = (x-2)(x+1)

note: the factor (x-2) is common between them take it one time

∴ LCM = (x-2)(x-6)(x+1)