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

Options 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

• The lcm of x^3+1 & x^3-1 is =(x^3-1)*(x^3+1)= (x^6-1) =((x^2))^3 - 1),i.e,((x^2))^3 - 1) is also a multiple of x^2-1.
  Hence lcm of x^3+1, x^2-1, x^3-1 will be (x^6-1)..
  Answer is OPTION 5) (x^6-1)
• 12 years agoHelpfull: Yes(15) No(3)
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• 12 years agoHelpfull: Yes(9) No(1)
• lcm of
  x^3+1=(x+1)(x^2+1-x)
  x^3-1=(x-1)(x^2+x+1)
  x^2-1=(x+1)(x-1)
  so lcm of these will be
  (x^2-1)(x^2+1-x)(x^2+x+1)
  (x^2-1)[(x^4+x^3+x^2+x^2+x+1-x^3-x^2-x)]
  (x^2-1)(x^4+x^2+1)
  (x^6+x^4+x^2-x^4-x^2-1)
  x^6-1(ans)
  
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• 12 years agoHelpfull: Yes(1) No(9)
• ans. (x^2-1)(x^2-x+1)(x^2+x+1) or x^6-1
  the factors of x^3+1 are (x+1)(x^2-x+1) and the factors of x^3-1 are (x-1)(x^2+x+1); the factors of x^2-1 are (x+1)(x-1). multiplying the common factors (x^2-1)(x^2-x+1)(x^2+x+1) the product is x^6-1.
• 12 years agoHelpfull: Yes(0) No(0)
• none of these
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