H.C.F. and L.C.M of polynomials

Let us consider 3 polynomials:

y1 = f1(x) = [(x-a)^m1]*[(x-b)^(n1+n2)]*[(x-c)]
y2 = f2(x) = [(x-a)^(m1+m2)]*[(x-b)^n1]*[(x-d)^p1]
y3 = f3(x) = [(x-a)]*[(x-c)^o1]*[(x-d)^(p1+p2)]

L.C.M. (y1, y2) = [(x-a)^(m1+m2)]*[(x-b)^(n1+n2)]*[(x-c)]*[(x-d)^p1]
H.C.F. (y1, y2) = [(x-a)^m1]*[(x-b)^n1]

L.C.M. (y1, y3) = [(x-a)^m1]*[(x-b)^(n1+n2)]*[(x-c)^o1]*[(x-d)^(p1+p2)]
H.C.F. (y1, y3) = [(x-a)]*[(x-c)]

L.C.M. (y2, y3) = [(x-a)^(m1+m2)]*[(x-b)^n1]*[(x-c)^o1]*[(x-d)^(p1+p2)]
H.C.F. (y2, y3) = [(x-a)]*[(x-d)^p1]

L.C.M. (y1, y2, y3) = [(x-a)^(m1+m2)]*[(x-b)^(n1+n2)]*[(x-c)^o1]*[(x-d)^(p1+p2)]
H.C.F. (y1, y2, y3) = [(x-a)]