lcm of x^3+1, x^2-1, x^3-1 will be

M4maths Previous Puzzles

21 Aug 2012 lcm

lcm of x^3+1, x^2-1, x^3-1 will be

OPtion

1) (x^2+x+1)(x^2-x+1)
2) (x^4-1)
3) (x^6-1)(x^2+1)
4) (x^6+1)(x^2-1)
5) (x^6-1)
6) (x^6+1)
7) (x^3+x^2+x+1)
8) (x-1)(x^2+1)(x+1)(x^2-1)
9) (x^4+1)
10) none of these

Solution

x^3+1 = (x+1)(x^2-x+1)
x^2-1 = (x+1)(x-1)
x^3-1 = (x-1)(x^2+x+1)
so lcm = (x+1)(x-1)(x^2+x+1)(x^2-x+1) = (x^3-1)(x^3+1) = (x^6-1)

Correct Option: 5 Best Solution (0)