### Examination Questions in HCF and LCM

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

- 4(x
^{ 4}- x^{ 2}+ 1) - 2(x
^{ 4}- x^{ 2}+ 1) - (x
^{ 4}- x^{ 2}+ 1) - None of the above

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

- None
- Infinitely many
- Less than 65
- Exactly one

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

- It is always 1
- It is always 2
- Either 1 or 2
- None of the above

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

- 1372
- 1398
- 1426
- 1484

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

- ab
- a
^{2}b^{2} - a
^{2}b^{2} - a
^{3}b^{2}

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

- x(x + 4)(x – 2)
^{ 2} - x(x + 4)(x – 2)
- x(x + 4)(x + 2)
^{ 2} - 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?

- HCF(a, bc) = 1
- HCF(a, bc) = a
- HCF(a, bc) = b
- None of the above

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

- 3
- 1
- 2
- 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?

- 3
- 5
- 6
- 8

10. What is the HCF of 36(3x^{4} + 5x^{3} – 2x^{2}), 9(6x^{3} + 4x^{2} – 2x), 54(27x^{4} – x)?

- 9x(x + 1)
- 9x(3x – 1)
- 18x(3x – 1)
- 18x(x + 1)

11. Consider the following statements :

- The HCF of x + y and x
^{10}– y^{10}is x + y. - The HCF of x + y and x
^{10}+ y^{10}is x + y. - The HCF of x – y and x
^{10}+ y^{10}is x – y. - The HCF of x – y and x
^{10}– y^{10}is x – y.

Which of the statements given above are correct?

- 1 and 2
- 2 and 3
- 1 and 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?

- x – 1
- x + 1
- x
^{2}– 1 - None of the above