LCM and HCF

Answer : D

Let the third expression be x^ay^bz^c
From the HCF, we can see that the power of x is 1. Therefore, to make sense, a should be 1.
From the LCM, we can see that the power of y and z are 5 and 4 respectively. Therefore, to make sense, b should be 5 and c should be 4.

Answer : C

x³ - x = x(x + 1)(x - 1)

x⁴ - 1 = (x² + 1)(x + 1)(x - 1)

We can see that there are four different terms from both expressions which are x, x+1, x-1 and x² + 1. And, the largest power of each of them is 1. Thus, the LCM is x(x + 1)(x - 1)(x² + 1).