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      Question

      The L.C.M of a² – 2a – 3 and a³ + a² + a + 1

      is 
      A (a + 2)(a - 3)(a² + 1) Correct Answer Incorrect Answer
      B (a + 1)(a - 3)(a² + 1) Correct Answer Incorrect Answer
      C (a + 1)(a - 3)(a² + 2) Correct Answer Incorrect Answer
      D (a + 1)(a - 2)(a² + 1) Correct Answer Incorrect Answer

      Solution

      Consider, the first expression a2 - ax - 3 Find the factors of first expression ⇒ a2 – 2a - 3 = (a - 3)(a + 1) Now, consider, the second expression a3 + a2 + a + 1 Find the factors of the second expression ⇒ a3 + a2 + a + 1 = a2 (a + 1) + (a + 1) ⇒ a3 + a2 + a + 1 = (a2 + 1)(a + 1) The common factors of the two expressions a2 – 2a - 3 and a3 + a2 + a + 1 is (a + 1) (a - 3) is extra factor in the first expression and (a2 + 1) are the extra factor in the second expression. Therefore, the required L.C.M. of  a2 – 2a – 3 and a3 + a2 + a + 1 is (a + 1)(a - 3)(a2 + 1).

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