Elementary MathematicsLCM and HCFmedium

LCM and HCF Quiz

Free practice quiz on LCM and HCF Quiz with detailed solutions for government exam preparation.

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About This Quiz

LCM and HCF Quiz is a free, 25-minute, 25-mark practice quiz on AajExam rated at medium difficulty, designed to help candidates preparing for SSC, UPSC, Banking, Railway and State PSC government competitive exams sharpen their command of LCM and HCF (Elementary Mathematics). Every question on this quiz ships with a detailed step-by-step solution so you don't just learn the right answer — you learn the reasoning and shortcuts top scorers use to crack similar questions faster on the actual exam day. Why LCM and HCF Quiz matters in your preparation: government exam-conducting bodies repeatedly draw questions from the same chapters and the same skill-clusters across recruitment cycles. By attempting focused topic-wise quizzes like this one, you build pattern recognition — the ability to spot which formula, rule or trick applies the moment you see a question. Toppers consistently report that 5-10 quizzes on a single topic delivers more exam-day score gain than 20+ unfocused full-length mocks, because targeted drilling exposes your specific sub-topic weaknesses with surgical precision. How to use this quiz effectively: attempt it in one sitting under the 25-minute timer, without referring to notes or external resources — simulate exam-day conditions exactly. After submission, review the auto-generated analytics to see your accuracy, time per question and section-wise performance. Then go through every wrong and skipped question with the explanation, mentally tagging the underlying concept rather than just memorising the answer. Revisit this quiz after 7-10 days; your second attempt should be 15-20% faster with noticeably better accuracy. Bookmark this page and revisit weekly as we add new quizzes on related topics. AajExam quiz design principles: every quiz on the platform is curated by subject experts using the actual question formats, difficulty distributions and time pressures of the target government exams. We deliberately avoid generic "textbook" questions in favour of exam-replicating ones. Solutions are written in plain English (and Hindi where source material was bilingual), with step-by-step working for quantitative problems, grammar rules for English questions, and direct reference statements for general awareness items. Performance analytics after each attempt include accuracy, attempt rate, time spent per question, and an estimated all-India percentile so you know exactly where you stand against other candidates. This quiz is completely free to attempt. You only need a free AajExam account to track your performance across attempts, view detailed solutions and unlock the platform-wide analytics dashboard. The platform is mobile-friendly and works seamlessly on smartphones, tablets and desktops — so you can sharpen your LCM and HCF (Elementary Mathematics) skills in any spare 15-minute window.

LCM and HCF Quiz — Questions with Solutions

All 25 questions from this quiz with the correct answer and explanation. Attempt them yourself first, then open each solution to check your reasoning.

  1. Q1.Find the LCM of 4 and 6.

    • A.8
    • B.10
    • C.12
    • D.24
    Show answer

    Answer: C. 12

    The least common multiple of 4 and 6 is 12.

  2. Q2.Find the HCF of 12 and 18.

    • A.4
    • B.6
    • C.8
    • D.12
    Show answer

    Answer: B. 6

    The highest common factor of 12 and 18 is 6.

  3. Q3.Find the LCM of 15 and 20.

    • A.30
    • B.45
    • C.60
    • D.90
    Show answer

    Answer: C. 60

    The LCM of 15 and 20 is 60.

  4. Q4.Find the HCF of 24 and 36.

    • A.6
    • B.8
    • C.12
    • D.18
    Show answer

    Answer: C. 12

    The HCF of 24 and 36 is 12.

  5. Q5.The product of two numbers is 240 and their HCF is 4. Find their LCM.

    • A.40
    • B.50
    • C.60
    • D.70
    Show answer

    Answer: C. 60

    LCM = Product / HCF = 240/4 = 60.

  6. Q6.Find the LCM of 8, 12 and 16.

    • A.24
    • B.36
    • C.48
    • D.64
    Show answer

    Answer: C. 48

    The LCM of 8, 12 and 16 is 48.

  7. Q7.Find the HCF of 15, 30 and 45.

    • A.5
    • B.10
    • C.15
    • D.20
    Show answer

    Answer: C. 15

    The HCF of 15, 30, and 45 is 15.

  8. Q8.Two numbers are in the ratio 3:4 and their HCF is 5. Find their LCM.

    • A.50
    • B.60
    • C.70
    • D.80
    Show answer

    Answer: B. 60

    Numbers are 15 and 20; LCM = 60.

  9. Q9.Find the smallest number divisible by 6, 8, and 12.

    • A.12
    • B.24
    • C.36
    • D.48
    Show answer

    Answer: B. 24

    The LCM of 6, 8, and 12 is 24.

  10. Q10.Find the largest number that divides 20 and 30 exactly.

    • A.5
    • B.10
    • C.15
    • D.20
    Show answer

    Answer: B. 10

    The HCF of 20 and 30 is 10.

  11. Q11.Find the LCM of 9 and 12.

    • A.18
    • B.24
    • C.36
    • D.72
    Show answer

    Answer: C. 36

    The LCM of 9 and 12 is 36.

  12. Q12.Find the HCF of 48 and 60.

    • A.6
    • B.12
    • C.18
    • D.24
    Show answer

    Answer: B. 12

    The HCF of 48 and 60 is 12.

  13. Q13.The LCM of two co-prime numbers is always equal to:

    • A.Their sum
    • B.Their product
    • C.Their difference
    • D.Zero
    Show answer

    Answer: B. Their product

    For co-prime numbers, LCM equals the product of the numbers.

  14. Q14.Find the LCM of 5, 10 and 15.

    • A.15
    • B.30
    • C.45
    • D.60
    Show answer

    Answer: B. 30

    The LCM of 5, 10, and 15 is 30.

  15. Q15.Find the HCF of 100 and 75.

    • A.15
    • B.20
    • C.25
    • D.30
    Show answer

    Answer: C. 25

    The HCF of 100 and 75 is 25.

  16. Q16.Two bells ring every 6 and 8 minutes respectively. If they ring together now, after how many minutes will they ring together again?

    • A.12 minutes
    • B.18 minutes
    • C.24 minutes
    • D.30 minutes
    Show answer

    Answer: C. 24 minutes

    This is the LCM of 6 and 8, which is 24.

  17. Q17.Find the LCM of 14 and 21.

    • A.28
    • B.35
    • C.42
    • D.56
    Show answer

    Answer: C. 42

    The LCM of 14 and 21 is 42.

  18. Q18.Find the HCF of 32 and 48.

    • A.8
    • B.16
    • C.24
    • D.32
    Show answer

    Answer: B. 16

    The HCF of 32 and 48 is 16.

  19. Q19.Which of the following pairs is co-prime?

    • A.8 and 9
    • B.6 and 8
    • C.10 and 15
    • D.12 and 18
    Show answer

    Answer: A. 8 and 9

    8 and 9 share no common factor other than 1, making them co-prime.

  20. Q20.Find the LCM of 6 and 10.

    • A.20
    • B.30
    • C.40
    • D.60
    Show answer

    Answer: B. 30

    The LCM of 6 and 10 is 30.

  21. Q21.Find the HCF of 45 and 60.

    • A.5
    • B.10
    • C.15
    • D.20
    Show answer

    Answer: C. 15

    The HCF of 45 and 60 is 15.

  22. Q22.The HCF of two numbers is 8 and their LCM is 48. If one number is 16, find the other.

    • A.20
    • B.22
    • C.24
    • D.26
    Show answer

    Answer: C. 24

    Other number = (HCF*LCM)/16 = (8*48)/16 = 24.

  23. Q23.Find the LCM of 3, 5 and 6.

    • A.15
    • B.20
    • C.30
    • D.45
    Show answer

    Answer: C. 30

    The LCM of 3, 5, and 6 is 30.

  24. Q24.Find the HCF of 21 and 28.

    • A.3
    • B.5
    • C.7
    • D.9
    Show answer

    Answer: C. 7

    The HCF of 21 and 28 is 7.

  25. Q25.Find the smallest number that is exactly divisible by 4, 5 and 6.

    • A.30
    • B.45
    • C.60
    • D.90
    Show answer

    Answer: C. 60

    The LCM of 4, 5 and 6 is 60.

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Frequently Asked Questions

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LCM and HCF Quiz runs on a 25-minute timer in real exam-style conditions. The clock starts the moment you click Start, mirroring the time pressure of the actual exam.

Are detailed solutions provided?

Yes. Every question on LCM and HCF Quiz ships with a complete step-by-step solution, the underlying concept, and (where applicable) shortcut tricks. You can also discuss any question with the AajExam community.

Can I attempt LCM and HCF Quiz multiple times?

Yes. You can attempt this quiz as many times as you like. Each attempt is recorded separately so you can track improvement in score, accuracy and time-management.

Which government exams does this quiz prepare me for?

LCM and HCF questions appear regularly in SSC CGL, CHSL, MTS, GD; IBPS PO, Clerk; SBI PO, Clerk; RRB NTPC, Group D; UPSC prelims and most State PSC exams. The specific weightage varies by exam — check the exam pattern on the corresponding AajExam exam page for details.