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TNPSC LCM and HCF practice questions with worked answers

By the PrepMatic team · Updated 9 Oct 2026 · 3 min read

HCF and LCM are named in the Group 4 aptitude syllabus, and their questions fall into a handful of repeating patterns: find the HCF or LCM, use the product rule, solve an events-together problem, or find a number that leaves a given remainder. Learn those four and you can handle nearly every question in this chapter. The five questions below are one of each. More on the whole subject is in TNPSC aptitude and mental ability.

What this topic covers

• Prime factorisation: the base of both HCF and LCM.
• HCF (greatest common divisor): the largest number that divides all the given numbers.
• LCM: the smallest number that all the given numbers divide.
• Word problems: bells, traffic lights and tiles use LCM; sharing equally and cutting into equal pieces use HCF.

Sample questions

Question 1

The HCF of 36 and 48 is:

• A. 12
• B. 6
• C. 18
• D. 24

Question 2

The LCM of 12, 15 and 20 is:

• A. 30
• B. 120
• C. 180
• D. 60

Question 3

The product of two numbers is 1,620 and their HCF is 9. Their LCM is:

• A. 90
• B. 162
• C. 180
• D. 1,800

Question 4

Three bells ring at intervals of 10, 15 and 25 minutes. They ring together at 8:00 AM. They will next ring together at:

• A. 10:00 AM
• B. 10:30 AM
• C. 9:30 AM
• D. 11:00 AM

Question 5

The smallest two-digit number that leaves a remainder of 5 when divided by 6, 8 and 12 is:

• A. 24
• B. 53
• C. 29
• D. 77

Answers and explanations

1. A. 36 = 2² × 3² and 48 = 2⁴ × 3. Take the smaller power of each common prime: 2² × 3 = 12.
2. D. 12 = 2² × 3, 15 = 3 × 5, 20 = 2² × 5. Take the highest power of every prime: 2² × 3 × 5 = 60.
3. C. HCF × LCM = product, so LCM = 1,620 ÷ 9 = 180.
4. B. 10 = 2 × 5, 15 = 3 × 5, 25 = 5². The LCM is 2 × 3 × 25 = 150 minutes, which is 2 hours 30 minutes. The next time is 8:00 AM + 2 h 30 min = 10:30 AM.
5. C. LCM(6, 8, 12) = 24, so the numbers leaving remainder 5 are 24k + 5: 5, 29, 53, 77 and so on. The smallest two-digit one is 29. Option A, 24, is divisible by all three and leaves remainder 0.

How to prepare LCM and HCF

Use prime factorisation as your single method. It handles HCF, LCM, products and even squares and cubes. The method is: factorise each number, then take the lowest powers for HCF and the highest powers for LCM. Practise on ten pairs of numbers until it is automatic.

Learn to recognise the word problem at a glance. "Together again", "at the same time", "next meeting" and "smallest number divisible by" suggest LCM. "Largest", "greatest number that divides", "cut into equal pieces" and "maximum size" suggest HCF. A two-second classification saves you from solving the wrong problem.

Practise the remainder family with its variants: remainder r with the same value in each case, which gives LCM plus r, and remainder different in each case, where the gap between divisor and remainder is the same, which gives LCM minus that gap. Question 5 is the first type.

For related arithmetic, go to TNPSC ratio and proportion practice and TNPSC time and work practice, where LCM is often used to pick a convenient total work.

Take the full topic test on PrepMatic

The best test for a chapter like this is timed repetition. Try a topic test on PrepMatic (about 15 questions, 30 minutes) and see how many of the questions you solve in under a minute. If you take mock tests too, the subject-wise breakdown will show how much aptitude is helping or hurting your total.

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