Here,
First expression = x2 + 2xy + y2 -z2
= (x + y)2 - z2
= (x + y + z) (x + y + z)
Second expression = y2 + 2yz + z2 - x2
= (y + z)2 - x2
= (x + y + z) (y + z - y)
Third expression = z2 + 2zx + x2 - y2
= (z + x)2 - y2
= (x + y + z) (x - y + z)
Therefore, HCF = (x + y + z)
And LCM = (x + y + z) (x + y - z) (y + z - x) (x - y + z)