Problems on H.C.F and L.C.M
- 1. What is the greatest number that divides 263, 935 and 1383 leaving a remainder of 7 in each case?
Options- A. 30
- B. 31
- C. 32
- D. 35 Discuss
Correct Answer: 32
Explanation:
The required greatest number is the HCF of 263-7, 935-7, 1383-7
i.e. 256, 928 and 1376 HCF = 32
- 2. If (x+2) is the HCF of x 2 + ax + b and x 2 + cx + d , then which one of the following is correct?
Options- A. a + c = b + d
- B. 2a + b = 2c + d
- C. b + 2c = 2a + d
- D. b - 2c = 2a - d Discuss
Correct Answer: b + 2c = 2a + d
Explanation:
If (x+2) is the HCF of x2 + ax + b and x2 + cx + d.
Then, (-2)2 -2a +b = (-2)2 -2c + d
b + 2c = 2a + d
- 3. Find the greatest possible length which can be used to measure 4m 3cm, 4m 34cm and 4m 65cm exactly.
Options- A. 31 cm
- B. 29 cm
- C. 28 cm
- D. 32 cm Discuss
Correct Answer: 31 cm
Explanation:
Required measure = HCF of 403, 434 and 465
= 31 cm
- 4. Which of the following fractions is the greatest of all? 7/8, 6/7, 4/5, 5/6?
Options- A. 6/7
- B. 4/5
- C. 5/6
- D. 7/8 Discuss
Correct Answer: 7/8
Explanation:
7 / 8 = 0.875,
6 / 7 = 0.857,
4 / 5 = 0.8 and 5/6 = 0.833
Now, 0.875 > 0.857 > 0.833 > 0.8
So, 7/8 is the greatest
- 5. L.C.M of 2/3, 4/9, 5/6 and 7/12 is?
Options- A. 1/18
- B. 1/36
- C. 35/9
- D. 140/3 Discuss
Correct Answer: 140/3
Explanation:
L.C.M = ( L.C.M . of 2, 4, 5, 7) / (H.C.F. of 3, 9, 6, 12)
= 140/3
- 6. L.C.M of 3/4, 6/7, 9/8 is?
Options- A. 18
- B. 3
- C. 3/56
- D. 9/28 Discuss
Correct Answer: 18
Explanation:
L. C . M = ( L.C.M of 3, 6, 9 ) / (H.C.F of 4, 7, 8)
= 18 / 1
= 18
- 7. H.C.F . of 1/2, 3/4, 5/6, 7/8, 9/10 is?
Options- A. 1/2
- B. 1/10
- C. 9/120
- D. 1/120 Discuss
Correct Answer: 1/120
Explanation:
H.C.F = ( H.C.F of 1, 3 , 5, 7, 9) / (L.C.M of 2, 4, 6, 8 , 10)
= 1 / 120
- 8. L.C.M of 3 3, 4, 4 2 and 3 is?
Options- A. 12
- B. 48
- C. 432
- D. None of these Discuss
Correct Answer: 432
Explanation:
L.C.M of 33, 4, 42 and 3 = L.C.M of 33 x 24
= 27 x 16
= 432
- 9. L.C.M of 87 and 145 is?
Options- A. 870
- B. 1305
- C. 435
- D. 1740 Discuss
Correct Answer: 435
Explanation:
H.C.F of 87 and 145 is 29
? L.C.M = ( 87 x 145) / 29
= 435
- 10. Which of the following is a pair of co-primes?
Options- A. (14, 35)
- B. (18, 25)
- C. (31, 93)
- D. (32, 62) Discuss
Correct Answer: (18, 25)
Explanation:
H.C.F . of 18 and 25 is 1
So, 18 and 25 are co-primes
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