I assume you mean to find (a) the GCF (greatest common factor) and (b) the least common multiple LCM.
To do both parts, you need ot factor the polynomials.
x^2 - 3x + 2 = (x - 2)(x - 1)
x^2 - 4x + 4 = (x - 2)(x - 2) = (x - 2)^2
(a) GCF: use only common factors with lower exponent.
The GCF is x - 2
(b) LCM: use common and not common factors with the larger exponent.
The LCM is (x - 2)^2(x - 1)