Question

find LCM :a^2+4a-12,a^2-5a+6 whose GCD is (a-2)​

Answer 1

Step-by-step explanation:

Let f(x) = a2 + 4a −12, g(x) = a2 −5a + 6.

f(x) = a2 + 4a −12

= a2 + 6a - 2a −12

= a(a + 6) - 2(a + 6)

f(x) = (a + 6)(a - 2)

g(x) = a2 −5a + 6

= a2 - 2a - 3a + 6

= a(a - 2) - 3(a - 6)

g(x) = (a - 3)(a - 2)

GCD is (a -2)

f (x) × g(x) = LCM × GCD

LCM = [f(x) × g(x)] / GCD

LCM = [(a + 6)(a - 2) (a - 3)(a - 2)] / a -2

LCM = (a + 6)(a - 2) (a - 3)