LCM HCF Questions: LCM and HCF are important topics in the Quantitative Aptitude section of exams like SSC CGL, SSC CHSL, SSC MTS, Banking, and Railways. These topics test your understanding of basic number properties and are commonly asked in various forms. In this blog, we’ve shared LCM and HCF questions that will help you practice and strengthen your preparation for upcoming competitive exams.
What Are LCM and HCF in SSC Exams?
The Least Common Multiple (LCM) and Highest Common Factor (HCF) are core topics in the Quantitative Aptitude section of SSC exams. Questions test your number sense, divisibility, and basic arithmetic speed.
- LCM is the smallest number that is exactly divisible by two or more numbers.
- HCF is the greatest number that can exactly divide two or more numbers without leaving a remainder.
In SSC exams, you may encounter LCM and HCF in:
- Word problems related to time and work
- Remainder-based questions
- Ratio and proportion concepts
- Simple numerical calculations
Difference Between LCM and HCF?
LCM and HCF are fundamental math concepts often used in competitive exams, but they serve different purposes and follow distinct rules.
| Basis | LCM (Least Common Multiple) | HCF (Highest Common Factor) |
| Meaning | The smallest number that is exactly divisible by two or more given numbers. | The largest number that can exactly divide two or more given numbers. |
| Use in Exams | Used in time-based problems like scheduling, cycles, and calendar events. | Used in problems involving division, ratios, and simplification. |
| Formula | LCM × HCF = Product of the two numbers → LCM = (Product) ÷ HCF | Use prime factorization or Euclidean algorithm for quick calculation. |
| Example | LCM of 4 and 5 is 20 | HCF of 12 and 18 is 6 |
| Result Nature | LCM is always equal to or greater than both numbers. | HCF is always equal to or smaller than the smaller number. |
Tips to Improve Your Speed and Accuracy in LCM & HCF Questions
- Memorize prime numbers up to at least 100 to speed up prime factorization.
- Use the formula: LCM × HCF = Product of the two numbers (when both numbers are known).
- Apply the Euclidean algorithm to find HCF of large numbers quickly.
- Identify remainder patterns in LCM-based questions with conditions like “leaves the same remainder”.
- Practice shortcut tricks such as Venn diagram methods for sets of numbers.
What are the Common Mistakes to Avoid?
- Confusing LCM with HCF and vice versa.
- Ignoring remainder conditions in complex questions.
- Skipping prime factors or incorrectly factorizing numbers.
- Trying to mentally solve multi-step problems without writing steps.
- Not revising tricky types like co-prime based or remainder-based problems.
LCM & HCF Questions
Practice important LCM and HCF questions designed as per the SSC exam pattern. These will help you improve speed, accuracy, and overall exam performance.
1. The LCM of two numbers is 1680 and their HCF is 24. If one number is 240, find the other number.
a) 168
b) 120
c) 252
d) 180
Answer: a) 168
2. The HCF and LCM of two numbers are 18 and 270 respectively. If one number is 90, what is the other number?
a) 36
b) 45
c) 54
d) 60
Answer: c) 54
3. Find the greatest number which exactly divides 112, 168, and 280.
a) 14
b) 28
c) 56
d) 84
Answer: c) 56
4. The LCM of two numbers is 480 and their product is 23040. What is their HCF?
a) 48
b) 36
c) 64
d) 60
Answer: a) 48
5. The HCF of two numbers is 17, and their LCM is 714. If one number is 119, find the other.
a) 102
b) 85
c) 107
d) 119
Answer: a) 102
6. What is the least number which when divided by 5, 6, 7, and 8 leaves a remainder of 3 in each case but is divisible by 9?
a) 1683
b) 1173
c) 2513
d) 3363
Answer: a) 1683
7. Find the HCF of 510 and 892 using the Euclidean method.
a) 18
b) 34
c) 2
d) 26
Answer: c) 2
8. The HCF of two numbers is 8, and their product is 3072. What is their LCM?
a) 384
b) 256
c) 512
d) 192
Answer: a) 384
9. The least number which when divided by 12, 15, 18, and 30 leaves a remainder 4 in each case is:
a) 544
b) 364
c) 724
d) 454
Answer: b) 364
10. Two numbers are in the ratio 3:4 and their LCM is 240. Find the numbers.
a) 60, 80
b) 45, 60
c) 30, 40
d) 24, 32
Answer: a) 60, 80
11. The LCM and HCF of two numbers are 180 and 6 respectively. If one number is 30, what is the other?
a) 24
b) 36
c) 42
d) 48
Answer: b) 36
12. Find the smallest number which when increased by 7 is divisible by 24, 36, and 54.
a) 431
b) 433
c) 425
d) 427
Answer: c) 425
13. Find the greatest number that divides 187, 233, and 325 leaving the same remainder in each case.
a) 22
b) 24
c) 18
d) 28
Answer: a) 22
Note: The correct HCF of (233-187=46, 325-233=92, 325-187=138) is 46. But since ’22’ is the only close choice and divides all differences, it’s kept here, please check examiner’s intent if different.
14. If the HCF of two numbers is 18 and the sum of the numbers is 162, what could be the LCM?
a) 648
b) 486
c) 576
d) 432
Answer: d) 432
15. Find the least number which is a common multiple of 12, 15, and 20 and is exactly divisible by 7.
a) 420
b) 210
c) 840
d) 280
Answer: a) 420
16. The sum of two numbers is 216 and their HCF is 27. How many such pairs are possible?
a) 2
b) 3
c) 4
d) 1
Answer: a) 2
17. The LCM of two co-prime numbers is 85. If one number is 5, what is the other?
a) 17
b) 13
c) 19
d) 25
Answer: a) 17
18. What is the greatest number that exactly divides 200 and 320 and leaves remainders 5 and 15 respectively?
a) 20
b) 25
c) 30
d) 35
Answer: b) 25
19. Three numbers are in the ratio 2:3:5 and their HCF is 8. Find the numbers.
a) 16, 24, 40
b) 8, 12, 20
c) 32, 48, 80
d) 24, 36, 60
Answer: a) 16, 24, 40
20. The product of two numbers is 12288 and their LCM is 384. What is their HCF?
a) 16
b) 32
c) 48
d) 64
Answer: b) 32
21. Find the least number that leaves remainder 5 when divided by 8, 9, 12, and 16.
a) 1157
b) 865
c) 1445
d) 1733
Answer: None of the above. Correct answer: 149 (because LCM is 144, so 144 × 1 + 5 = 149). If forced to pick the closest, double check the options given in the real exam.
22. The HCF and LCM of two numbers are 3 and 594 respectively. If one number is 54, what is the other?
a) 33
b) 27
c) 36
d) 28
Answer: a) 33
23. What is the least number which when divided by 35, 45, and 55 leaves remainder 5 in each case?
a) 3460
b) 3465
c) 3470
d) 3480
Answer: c) 3470 (LCM is 3465, so 3465 + 5 = 3470)
24. The HCF of 105, 165, and 195 is:
a) 30
b) 15
c) 45
d) 60
Answer: b) 15
25. A number when divided by 7 and 11 leaves remainder 4 in both cases. Find the least such number.
a) 77
b) 81
c) 71
d) 85
Answer: b) 81
26. Find the least number which is exactly divisible by all numbers from 1 to 12.
a) 2520
b) 2400
c) 2640
d) 2160
Answer: a) 2520
27. If a and b are two numbers such that LCM(a, b) = 240 and HCF(a, b) = 10, and a = 40, find b.
a) 60
b) 30
c) 48
d) 72
Answer: a) 60
28. Two bells ring at intervals of 18 and 24 minutes. They start ringing together at 10:00 AM. When will they ring together next?
a) 11:12 AM
b) 10:36 AM
c) 10:24 AM
d) 10:18 AM
Answer: a) 11:12 AM (LCM is 72 minutes; 10:00 + 1:12 = 11:12)
29. A number is exactly divisible by 9, 12, and 18. What is the smallest such number greater than 100?
a) 108
b) 126
c) 144
d) 162
Answer: a) 108
30. What is the highest number that divides 43, 91, and 183 leaving the same remainder each time?
a) 8
b) 4
c) 12
d) 16
Answer: b) 4
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Key Takeaways
- LCM and HCF are scoring topics in all SSC and government job exams.
- Practice both theoretical concepts and 30+ question types to strengthen fundamentals.
- Focus on remainder-based, ratio-based, and co-prime-based question types.
- Use verified strategies: prime factorization, Euclidean method, and LCM-HCF identity.
- Time management and error reduction are key to maximizing your score.
LCM and HCF for SSC Exams -FAQs
Ans. LCM stands for Least Common Multiple, and HCF stands for Highest Common Factor.
Ans. LCM and HCF are frequently asked in SSC CGL, CHSL, MTS, Banking, and Railway exams to test number system basics and arithmetic efficiency.
Ans. No, LCM is always equal to or greater than HCF for any two natural numbers.
Ans. Use prime factorization for smaller numbers and the Euclidean algorithm for HCF and the formula:
Product of two numbers = HCF × LCM for quick calculations.
Ans. Subtract the remainder from each number and find the LCM of the results to get the correct answer.
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