SSC CGL HCF and LCM Verified Practice Test 1

15 structurally validated HCF and LCM questions with unique options, mapped answers and explanations.

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SSC CGL Practice Session

SSC CGL HCF and LCM Verified Practice Test 1

15 structurally validated HCF and LCM questions with unique options, mapped answers and explanations.

Questions

Marking

+2 correct, -0.5 wrong

Format

15-question practice session

Preview all 15 questions in SSC CGL HCF and LCM Verified Practice Test 1 (no login required)

HCF and LCM
1. The HCF of 84 and 126 is:
- A. 21
- B. 28
- C. 42 (Correct)
- D. 63
Explanation: 84 = 2 x 2 x 3 x 7 and 126 = 2 x 3 x 3 x 7. Common product = 2 x 3 x 7 = 42.
LCM
2. The LCM of 18, 24 and 30 is:
- A. 180
- B. 240
- C. 360 (Correct)
- D. 720
Explanation: 18 = 2 x 3^2, 24 = 2^3 x 3, 30 = 2 x 3 x 5. LCM = 2^3 x 3^2 x 5 = 360.
Product Relation
3. The HCF and LCM of two numbers are 12 and 240. If one number is 48, the other number is:
- A. 48
- B. 60 (Correct)
- C. 72
- D. 80
Explanation: Product of numbers = HCF x LCM = 2880. Other number = 2880 / 48 = 60.
HCF Word Problem
4. Three wires of lengths 96 m, 120 m and 144 m are cut into equal pieces with no length left. The greatest possible length of each piece is:
- A. 12 m
- B. 18 m
- C. 24 m (Correct)
- D. 36 m
Explanation: The greatest equal piece length is the HCF of 96, 120 and 144, which is 24.
LCM Word Problem
5. Three bells ring at intervals of 12, 15 and 20 minutes. If they ring together at 9:00 AM, when will they next ring together?
- A. 9:30 AM
- B. 10:00 AM (Correct)
- C. 10:15 AM
- D. 11:00 AM
Explanation: LCM of 12, 15 and 20 is 60 minutes, so they ring together again at 10:00 AM.
HCF
6. The largest number that divides 135 and 180 exactly is:
- A. 15
- B. 30
- C. 45 (Correct)
- D. 60
Explanation: The HCF of 135 and 180 is 45.
LCM
7. The least number which is exactly divisible by 16, 20 and 24 is:
- A. 120
- B. 160
- C. 240 (Correct)
- D. 480
Explanation: 16 = 2^4, 20 = 2^2 x 5, 24 = 2^3 x 3. LCM = 2^4 x 3 x 5 = 240.
HCF and Remainder
8. The greatest number that divides 43, 91 and 183 leaving the same remainder in each case is:
- A. 4 (Correct)
- B. 8
- C. 16
- D. 24
Explanation: Take differences: 91 - 43 = 48, 183 - 91 = 92, and 183 - 43 = 140. HCF of 48, 92 and 140 is 4.
HCF and Remainder
9. The greatest number that divides 55, 127 and 175 leaving the same remainder is:
- A. 12
- B. 18
- C. 24 (Correct)
- D. 36
Explanation: Take differences: 127 - 55 = 72, 175 - 127 = 48, and 175 - 55 = 120. HCF of 72, 48 and 120 is 24.
Co-prime
10. Which pair is co-prime?
- A. 21 and 35
- B. 28 and 45 (Correct)
- C. 32 and 48
- D. 42 and 63
Explanation: 28 = 2^2 x 7 and 45 = 3^2 x 5, so their HCF is 1.
HCF and LCM
11. Two numbers are in the ratio 5:7 and their HCF is 9. Their LCM is:
- A. 315 (Correct)
- B. 405
- C. 525
- D. 630
Explanation: Numbers are 45 and 63. Their LCM = 45 x 63 / 9 = 315.
LCM
12. The least 4-digit number divisible by 18, 24 and 36 is:
- A. 1008 (Correct)
- B. 1080
- C. 1152
- D. 1224
Explanation: LCM of 18, 24 and 36 is 72. The least 4-digit multiple of 72 is 72 x 14 = 1008.
HCF
13. If the HCF of 72 and x is 18, which of the following can be x?
- A. 36
- B. 45
- C. 60
- D. 90 (Correct)
Explanation: HCF(72, 90) = 18. The other choices give HCF values 36, 9 and 12 respectively.
HCF
14. If the HCF of 72 and x is 24, which of the following can be x?
- A. 48 (Correct)
- B. 54
- C. 60
- D. 90
Explanation: HCF(72, 48) = 24. The other choices give HCF 18, 12 and 18 respectively.
Product Relation
15. The product of two numbers is 2160 and their HCF is 12. Which of the following can be their LCM?
- A. 120
- B. 150
- C. 180 (Correct)
- D. 240
Explanation: For two numbers, product = HCF x LCM. Therefore LCM = 2160 / 12 = 180.