When it comes to aptitude tests in companies like TCS, Infosys, Accenture, Capgemini, and Wipro, one topic that never fails to appear is LCM and HCF.

If you’re preparing for any campus placement, understanding the logic behind these two simple concepts can help you easily solve at least 3–4 marks worth of questions.

This blog covers the complete “LCM & HCF One Shot” practice set — directly inspired from real company exams — along with options, correct answers, and reasoning.

LCM & HCF Key Concepts

  • HCF (Highest Common Factor): The largest number that divides two or more numbers exactly.

  • LCM (Least Common Multiple): The smallest number that is a multiple of two or more numbers.

Formula:

HCF × LCM = Product of the Numbers\text{HCF × LCM = Product of the Numbers}

LCM and HCF Aptitude Questions with Answers

Q1.

HCF of two numbers 12906 and 14818 is 478. Find their LCM.

Options:
a) 200043
b) 600129
c) 800172
d) 400086

Answer: ✅ b) 600129

Explanation:

LCM=12906×14818478=600129\text{LCM} = \frac{12906 × 14818}{478} = 600129

Q2.

The LCM of two numbers is 1920 and their HCF is 16. If one number is 128, find the other number.

Options:
a) 204
b) 240
c) 260
d) 320

Answer: ✅ b) 240

Explanation:

LCM × HCF = Product of Numbers\text{LCM × HCF = Product of Numbers}

→ 1920 × 16 = 128 × x → x = 240

Q3.

The LCM of two numbers is 864 and their HCF is 144. If one number is 288, find the other number.

Options:
a) 576
b) 1296
c) 432
d) 144

Answer: ✅ c) 432

Explanation:

x=864×144288=432x = \frac{864 × 144}{288} = 432

Q4.

The ratio of two numbers is 4 : 5 and their HCF is 8. Find their LCM.

Options:
a) 130
b) 140
c) 150
d) 160

Answer: ✅ d) 160

Explanation:
Numbers = 8×4 = 32 and 8×5 = 40
→ LCM = 160

Q5.

The ratio of two numbers is 4 : 5 and their LCM is 120. The numbers are:

Options:
a) 30, 40
b) 40, 32
c) 24, 30
d) 36, 20

Answer: ✅ a) 30, 40

Explanation:
Let numbers = 4x and 5x → LCM = 20x
20x = 120 → x = 6 → Numbers = 24, 30
(Typo corrected from PPT)

Q6.

If the ratio of two numbers is 2 : 3 and their LCM is 54, find the sum of the two numbers.

Options:
a) 5
b) 15
c) 45
d) 270

Answer: ✅ c) 45

Explanation:
Numbers = 2x, 3x → LCM = 6x → 6x = 54 → x = 9
Sum = 2x + 3x = 45

Q9.

Find the LCM of 1.6, 0.04, and 0.005.

Options:
a) 3.2
b) 0.06
c) 1.06
d) 1.6

Answer: ✅ a) 3.2

Explanation:
Convert to integers → 16, 4, 0.5 → Simplify and LCM = 3.2

Q10.

Find the LCM of 1.2, 0.24, and 6.

Options:
a) 0.006
b) 0.06
c) 0.36
d) 6

Answer: ✅ d) 6

Explanation:
Multiples of 6 already include 1.2 and 0.24 → LCM = 6

Q11.

Find the HCF of 1.7, 0.51, and 0.153.

Options:
a) 0.017
b) 0.17
c) 0.18
d) 0.175

Answer: ✅ a) 0.017

Q12.

Four bells ring at intervals of 5, 6, 8, and 9 seconds. They all ring together at some time. After how many seconds will they ring together again?

Options:
a) 6 minutes
b) 12 minutes
c) 18 minutes
d) 24 minutes

Answer: ✅ b) 12 minutes

Explanation:
LCM of (5,6,8,9) = 360 seconds = 6 minutes.

Q13.

Four bells ring at intervals of 30 minutes, 1 hour, 1.5 hours, and 1 hour 45 minutes. All ring together at 12 noon. When will they ring together again?

Options:
a) 12 midnight
b) 3 a.m.
c) 6 a.m.
d) 9 a.m.

Answer: ✅ c) 6 a.m.

Explanation:
LCM of (30, 60, 90, 105) = 360 minutes = 6 hours → 12 + 6 = 6 a.m.

Q15.

The traffic lights at three different crossings change after 24, 36, and 54 seconds respectively. If they all change simultaneously at 10:15:00 AM, when will they change together again?

Options:
a) 10:16:54 AM
b) 10:18:36 AM
c) 10:17:02 AM
d) 10:22:12 AM

Answer: ✅ b) 10:18:36 AM

Explanation:
LCM(24, 36, 54) = 216 seconds = 3 min 36 sec → 10:15 + 3:36 = 10:18:36 AM

Q16.

A track is 120m long. Two people, A and B, run around it at 12 m/min and 20 m/min respectively in the same direction. When will they meet again at the starting point?

Answer: ✅ 15 minutes

Explanation:
Relative speed = (20 – 12) = 8 m/min
LCM of (120/12, 120/20) = 10 & 6 → LCM = 30 min for full round, but they meet every 15 minutes.

Q17.

The product of two numbers is 2028 and their HCF is 13. The number of such pairs is:

Options:
a) 1
b) 2
c) 3
d) 4

Answer: ✅ c) 3

Explanation:
Let numbers = 13x, 13y → xy = 12 → Possible coprime pairs: (1,12), (3,4), (2,6)

Q18.

The product of two numbers is 2160 and their HCF is 12. The number of such pairs is:

Options:
a) 1
b) 2
c) 3
d) 4

Answer: ✅ b) 2

Explanation:
xy = 15 → coprime pairs (1,15), (3,5)

Q19.

Find the greatest number which on dividing 1661 and 2045 leaves remainders 10 and 13 respectively.

Options:
a) 125
b) 127
c) 129
d) 131

Answer: ✅ b) 127

Explanation:
Difference = (2045 – 13) – (1661 – 10) = 2032 – 1651 = 381 → HCF(381,127) = 127

Q20.

A fruit vendor brings 1092 apples and 3432 oranges. He arranges them in equal heaps with maximum fruits per heap. How many fruits per heap?

Options:
a) 104
b) 124
c) 156
d) 178

Answer: ✅ c) 156

Explanation:
HCF(1092, 3432) = 156

Key Takeaways

  1. Remember: HCF × LCM = Product of the Numbers

  2. For ratio-based questions, convert ratio → numbers by multiplying with HCF.

  3. Always simplify decimals by converting into integers before LCM/HCF.

  4. Bell and traffic light problems = LCM-based time calculation.

  5. Practice questions daily — these are among the easiest high-scoring aptitude problems.

Conclusion

The LCM and HCF chapter is a must-practice topic for all placement aspirants. These 20 curated questions cover every pattern Infosys, TCS, Capgemini, Wipro, and Accenture have asked in the last few years.

Master these, and you’ll secure full marks in this section confidently.