Examination Questions in HCF and LCM

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1. What is the HCF of 8(x 5 - x 3 + x) and 28(x 6 + 1)?

  1. 4(x 4 - x 2 + 1)
  2. 2(x 4 - x 2 + 1)
  3. (x 4 - x 2 + 1)
  4. None of the above

2. What is the number of integral solutions of the equations HCF (a, b) = 5 and a + b = 65?

  1. None
  2. Infinitely many
  3. Less than 65
  4. Exactly one

3. For any integers ‘a’ and ‘b’ with HCF (a, b) = 1, what is HCF (a + b, a – b) equal to?

  1. It is always 1
  2. It is always 2
  3. Either 1 or 2
  4. None of the above

4. The HCF of two numbers is 98 and their LCM is 2352. The sum of the numbers may be

  1. 1372
  2. 1398
  3. 1426
  4. 1484

5. What is the HCF of a 2 b 4 + 2a 2 b 2 and (ab) 7 – 4a 2 b 9?

  1. ab
  2. a 2 b2
  3. a 2 b2
  4. a 3 b2

6. What is the LCM of x 2 +2x – 8, x 3 - 4x 2 + 4x and x 2 + 4x?

  1. x(x + 4)(x – 2) 2
  2. x(x + 4)(x – 2)
  3. x(x + 4)(x + 2) 2
  4. x(x + 4) 2(x – 2)

7. For integers a, b and c, if HCF(a, b) = 1 and HCF(a, c) = 1, then which one of the following is correct?

  1. HCF(a, bc) = 1
  2. HCF(a, bc) = a
  3. HCF(a, bc) = b
  4. None of the above

8. For any integer n, what is the HCF of integers m = 2n + 1 and k = 9n + 4?

  1. 3
  2. 1
  3. 2
  4. 4

9. If (x – 6) is the HCF of x 2 – 2x – 24 and x 2 – kx – 6, then what is the value of k?

  1. 3
  2. 5
  3. 6
  4. 8

10. What is the HCF of 36(3x4 + 5x3 – 2x2), 9(6x3 + 4x2 – 2x), 54(27x4 – x)?

  1. 9x(x + 1)
  2. 9x(3x – 1)
  3. 18x(3x – 1)
  4. 18x(x + 1)

11. Consider the following statements :

  1. The HCF of x + y and x10 – y10 is x + y.
  2. The HCF of x + y and x10 + y10 is x + y.
  3. The HCF of x – y and x10 + y10 is x – y.
  4. The HCF of x – y and x10 – y10 is x – y.

Which of the statements given above are correct?

  1. 1 and 2
  2. 2 and 3
  3. 1 and 4
  4. 2 and 4

12. What is the HCF of the polynomials x 4 – 3x + 2, x 3 – 3x 2 + 3x – 1 and x 4 – 1?

  1. x – 1
  2. x + 1
  3. x2 – 1
  4. None of the above