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About HCF & LCM — Class 6 ICSE

Learn to find the highest common factor and lowest common multiple using prime factorization. This topic is part of the ICSE Class 6 mathematics syllabus (chapter: Chapter 2). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in HCF & LCM

  • Factors and Multiples
  • Prime and Composite Numbers
  • Prime Factorization
  • Highest Common Factor (HCF)
  • Lowest Common Multiple (LCM) and the HCF-LCM Relationship

Interactive lesson · about 20 minutes · checkpoint question after every unit

HCF & LCM — solved examples for Class 6 ICSE

Example 1easy

Which of the following is a prime number?
  1. A)15
  2. B)21
  3. C)29
  4. D)35

Step-by-step solution

  1. Check each number: 15 = 3 × 5, 21 = 3 × 7, 35 = 5 × 7.
  2. 29 has no factors other than 1 and 29, so it is prime.

Answer: 29

Example 2medium

Find the HCF of 48, 72, and 120 using prime factorization.
  1. A)12
  2. B)24
  3. C)8
  4. D)6

Step-by-step solution

  1. 48 = 2⁴ × 3, 72 = 2³ × 3², 120 = 2³ × 3 × 5.
  2. Common primes with lowest powers: 2³ × 3 = 8 × 3 = 24.
    HCF=24HCF = 24

Answer: 24

Example 3hard

Find the smallest number which when divided by 8, 12, and 15 leaves a remainder 5 in each case.
  1. A)125
  2. B)245
  3. C)365
  4. D)485

Step-by-step solution

  1. LCM(8, 12, 15): 8 = 2³, 12 = 2² × 3, 15 = 3 × 5.
    LCM=23×3×5=120LCM = 2³ × 3 × 5 = 120
  2. Add the remainder:
    120+5=125120 + 5 = 125

Answer: 125

Practice questions on HCF & LCM

  1. Q1.easy

    Find the prime factorization of 36.
    1. A)2² × 3²
    2. B)2³ × 3
    3. C)4 × 9
    4. D)6 × 6
    Show answer

    Answer: 2² × 3²

    Hint: Break 36 into its smallest prime factors by dividing repeatedly.

  2. Q2.easy

    Find the HCF of 12 and 18.
    1. A)2
    2. B)3
    3. C)6
    4. D)12
    Show answer

    Answer: 6

    Hint: List the factors of both numbers and find the greatest common one.

  3. Q3.easy

    Find the LCM of 4 and 6.
    1. A)2
    2. B)12
    3. C)24
    4. D)6
    Show answer

    Answer: 12

    Hint: LCM is the smallest number that is a multiple of both 4 and 6.

  4. Q4.medium

    Find the LCM of 15, 20, and 30.
    1. A)60
    2. B)120
    3. C)300
    4. D)30
    Show answer

    Answer: 60

    Hint: Use prime factorization: 15 = 3 × 5, 20 = 2² × 5, 30 = 2 × 3 × 5.

  5. Q5.medium

    If HCF(a, b) = 6 and LCM(a, b) = 60, and a = 12, find b.
    1. A)20
    2. B)30
    3. C)15
    4. D)10
    Show answer

    Answer: 30

    Hint: Use the relation: HCF × LCM = a × b.

  6. Q6.medium

    Two bells ring at intervals of 8 minutes and 12 minutes respectively. If they ring together at 9:00 AM, when will they next ring together?
    1. A)9:20 AM
    2. B)9:24 AM
    3. C)9:36 AM
    4. D)9:48 AM
    Show answer

    Answer: 9:24 AM

    Hint: Find the LCM of 8 and 12. That gives the time interval before they ring together again.

  7. Q7.hard

    The HCF of two numbers is 18 and their LCM is 360. If one number is 72, find the other.
    1. A)90
    2. B)180
    3. C)45
    4. D)108
    Show answer

    Answer: 90

    Hint: Use: HCF × LCM = Product of the two numbers.

  8. Q8.hard

    Find the greatest number that divides 180 and 264 leaving remainders 4 and 6 respectively.
    1. A)22
    2. B)44
    3. C)11
    4. D)88
    Show answer

    Answer: 22

    Hint: Subtract the respective remainders from each number, then find HCF.

  9. Q9.hard

    Three alarm clocks ring at intervals of 6, 9, and 12 minutes. If they all ring together at noon, when will they next ring together?
    1. A)12:18 PM
    2. B)12:36 PM
    3. C)12:24 PM
    4. D)12:54 PM
    Show answer

    Answer: 12:36 PM

    Hint: Find the LCM of 6, 9, and 12.

These are 9 of the 60 questions available for HCF & LCM. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.