Let’s find the G.C.D and L.C.M. of the following expressions:

a³-4a² + 4a, a² + a-6, a³-8

Factors of a³-4a² + 4a

=a(a²-4a + 4)

=a(a-2)²

Factors of a² + a-6

= a² + 3a-2a-6

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

=(a + 3)(a-2)

Factors of a³-8

=(a-2)(a² + 2a + 4)

LCM is the lowest common multiple, which is the product of all the common factors taken once and the remaining factors as it is.

∴ the LCM of a³-4a² + 4a, a² + a-6, a³-8 is a(a-2)²(a² + 2a + 4) (a + 3)

GCD is the greatest common divisor, which is equal to the product of all the common divisors.

∴ the GCD is (a-2)