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About HCF & LCM — Class 7 CBSE

Find highest common factor and lowest common multiple of numbers. This topic is part of the CBSE Class 7 mathematics syllabus (chapter: Chapter 11). 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

  • Introduction to Factors, Multiples, HCF & LCM
  • Finding HCF & LCM using Prime Factorization Method
  • Finding HCF & LCM using Division Method
  • Relation between HCF & LCM and Word Problems
  • Summary, Connections, and Preparation for Practice

Interactive lesson · about 15 minutes · checkpoint question after every unit

HCF & LCM — solved examples for Class 7 CBSE

Example 1easy

Which of the following statements about factors and multiples is TRUE?
  1. A)A) Every number has an infinite number of factors.
  2. B)B) Every multiple of a number is greater than or equal to the number itself.
  3. C)C) The only common factor of two prime numbers is their product.
  4. D)D) The smallest multiple of every number is 1.

Step-by-step solution

  1. Factors are limited, meaning a number has a finite set of factors. Multiples are infinite. So, option A is false.
  2. The smallest multiple of any natural number (except 0) is the number itself. All other multiples are greater than the number. So, option B is true.
  3. The only common factor of two prime numbers is 1, as prime numbers only have 1 and themselves as factors. So, option C is false.
  4. The smallest multiple of every number is the number itself, not 1 (unless the number is 1). So, option D is false.

Answer: B) Every multiple of a number is greater than or equal to the number itself.

Example 2medium

Find the Highest Common Factor (HCF) of 72, 108, and 180 using the prime factorization method.
  1. A)12
  2. B)18
  3. C)36
  4. D)72

Step-by-step solution

  1. Prime factorization of 72: 2 × 2 × 2 × 3 × 3 = 2³ × 3²
  2. Prime factorization of 108: 2 × 2 × 3 × 3 × 3 = 2² × 3³
  3. Prime factorization of 180: 2 × 2 × 3 × 3 × 5 = 2² × 3² × 5
  4. Common prime factors are 2 and 3. The lowest power of 2 is 2² and the lowest power of 3 is 3². HCF = 2² × 3² = 4 × 9 = 36.

Answer: 36

Example 3hard

What is the HCF of 108, 162, and 198?
  1. A)6
  2. B)18
  3. C)36
  4. D)54

Step-by-step solution

  1. Find the prime factorization of each number:
  2. 108 = 2² × 3³
  3. 162 = 2 × 3⁴
  4. 198 = 2 × 3² × 11
  5. To find the HCF, take the lowest power of each common prime factor. The common prime factors are 2 and 3.
  6. Lowest power of 2 is 2¹.
    21=22¹ = 2
  7. Lowest power of 3 is 3².
    32=93² = 9
  8. HCF = 2 × 3² = 2 × 9 = 18.

Answer: 18

Practice questions on HCF & LCM

  1. Q1.easy

    Rohan tried to find the prime factorization of 72. His steps are: 72 = 2 × 36, 36 = 3 × 12, 12 = 2 × 6, 6 = 2 × 3. He concluded 72 = 2 × 3 × 2 × 2 × 3. What is the error in Rohan's prime factorization process?
    1. A)A) He did not find any error; the factorization is correct.
    2. B)B) The number 36 is not a prime factor.
    3. C)C) He listed 3 twice as a prime factor.
    4. D)D) He did not consistently break down composite factors into only prime factors at each stage.
    Show answer

    Answer: D) He did not consistently break down composite factors into only prime factors at each stage.

    Hint: Remember that prime factorization involves breaking down numbers into *only* prime factors. Check if all intermediate numbers were fully broken down immediately.

  2. Q2.easy

    Which of the following statements correctly defines the Highest Common Factor (HCF) of two or more numbers?
    1. A)A) The HCF is the largest number that divides each of the given numbers exactly.
    2. B)B) The HCF is the smallest number that is a multiple of all the given numbers.
    3. C)C) The HCF is the product of all prime factors common to the numbers.
    4. D)D) The HCF is the largest prime number that divides at least one of the given numbers.
    Show answer

    Answer: A) The HCF is the largest number that divides each of the given numbers exactly.

    Hint: Think about what 'factor' means and what 'common' and 'highest' imply in the context of division.

  3. Q3.easy

    Which of the following statements correctly defines the Least Common Multiple (LCM) of two or more numbers?
    1. A)A) The LCM is the largest number that divides each of the given numbers exactly.
    2. B)B) The LCM is the smallest number that is a multiple of all the given numbers.
    3. C)C) The LCM is the product of the highest powers of all prime factors involved in the numbers.
    4. D)D) The LCM is the smallest prime number that divides all the given numbers.
    Show answer

    Answer: B) The LCM is the smallest number that is a multiple of all the given numbers.

    Hint: Consider what 'multiple' means and what 'common' and 'least' imply in the context of multiplication.

  4. Q4.medium

    What is the Least Common Multiple (LCM) of 24, 36, and 40?
    1. A)120
    2. B)240
    3. C)360
    4. D)720
    Show answer

    Answer: 360

    Hint: Use the prime factorization method or the common division method. For LCM, consider all prime factors raised to their highest power.

  5. Q5.medium

    A shopkeeper has 144 pens and 216 pencils. He wants to pack them into identical boxes such that each box has the same number of pens and the same number of pencils. What is the maximum number of boxes he can make?
    1. A)12
    2. B)24
    3. C)36
    4. D)72
    Show answer

    Answer: 72

    Hint: To find the maximum number of identical groups, you need to find the HCF of the given quantities.

  6. Q6.medium

    Three bells ring at intervals of 15 minutes, 20 minutes, and 30 minutes, respectively. If they all ring together at 10:00 AM, at what time will they next ring together?
    1. A)10:30 AM
    2. B)11:00 AM
    3. C)11:30 AM
    4. D)12:00 PM
    Show answer

    Answer: 11:00 AM

    Hint: To find when they will next ring together, you need to find the LCM of their ringing intervals.

  7. Q7.hard

    Three bells ring at intervals of 12 minutes, 15 minutes, and 20 minutes respectively. If they all ring together at 8:00 AM, at what time will they next ring together, and how many times will the bell with the shortest interval have rung by then (excluding the 8:00 AM ring)?
    1. A)9:00 AM, 5 times
    2. B)9:00 AM, 6 times
    3. C)10:00 AM, 5 times
    4. D)10:00 AM, 6 times
    Show answer

    Answer: 9:00 AM, 5 times

    Hint: To find when they ring together again, calculate the LCM of their ringing intervals. Then, use this time to find how many times the fastest bell rang.

  8. Q8.hard

    The HCF of two numbers is 18 and their LCM is 540. If one of the numbers is 108, what is the sum of the digits of the other number?
    1. A)3
    2. B)6
    3. C)9
    4. D)12
    Show answer

    Answer: 9

    Hint: Remember the fundamental relationship between the HCF, LCM, and the product of two numbers. Once you find the other number, don't forget the final step!

  9. Q9.hard

    A confectioner has 300 ladoos and 252 gulab jamuns. He wants to arrange them in trays such that each tray contains the maximum possible number of sweets of the same kind, and no sweets are left over. What is the maximum number of sweets in each tray, and how many trays will be required in total?
    1. A)12 sweets, 46 trays
    2. B)12 sweets, 47 trays
    3. C)24 sweets, 23 trays
    4. D)24 sweets, 24 trays
    Show answer

    Answer: 12 sweets, 46 trays

    Hint: The 'maximum possible number' points towards finding the HCF. After finding the HCF, calculate the number of trays for each type of sweet and then sum them up.

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.