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HCF and LCM for Grade 6: Easy Explanation with Examples

HCF and LCM for Grade 6 are important maths topics that help students understand factors and multiples. Many students find them confusing at first, but they become much easier when you understand their meanings and follow simple steps. In this guide, you will learn how to find HCF and LCM using prime factorization, solve examples, and practise questions with answers.

1. What Is HCF? (Highest Common Factor)

HCF stands for Highest Common Factor.

It is the greatest number that divides two or more numbers exactly, without leaving a remainder.

Example: Find the HCF of 12 and 18.

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6

The highest common factor is 6.

Therefore, HCF of 12 and 18 = 6.

2. What Is LCM? (Lowest Common Multiple)

LCM stands for Lowest Common Multiple.

It is the smallest number that is a multiple of two or more numbers.

Example: Find the LCM of 4 and 6.

Multiples of 4: 4, 8, 12, 16, 20, 24

Multiples of 6: 6, 12, 18, 24, 30

The smallest common multiple is 12.

Therefore, LCM of 4 and 6 = 12.

3. Difference Between HCF and LCM for Grade 6

It is important to remember the difference:

  • HCF is the greatest factor shared by the numbers.
  • LCM is the smallest multiple shared by the numbers.

Easy way to remember:

HCF = Greatest common factor.

LCM = Smallest common multiple.

4. How to Find HCF and LCM Using Prime Factorization

Prime factorization means writing a number as a product of prime numbers.

Prime numbers include 2, 3, 5, 7, 11 and 13.

Let’s learn the method step by step.

Example: Find the HCF and LCM of 12 and 18.

Step 1: Find the prime factors.

12 = 2 × 2 × 3

18 = 2 × 3 × 3

Step 2: Find the HCF.

Choose the prime factors that are common to both numbers, using the smallest power of each.

Common factors = 2 × 3

HCF = 6

Step 3: Find the LCM.

Choose all the prime factors that appear in either number, using the greatest power of each.

LCM = 2 × 2 × 3 × 3

LCM = 36

Final answer:

HCF = 6

LCM = 36

5. HCF and LCM Examples for Grade 6

Find the HCF and LCM of 24 and 36.

Step 1: Prime factorization

24 = 2 × 2 × 2 × 3

36 = 2 × 2 × 3 × 3

Step 2: Find the HCF

Common prime factors with the smallest powers:

HCF = 2 × 2 × 3 = 12

Step 3: Find the LCM

All prime factors with the greatest powers:

LCM = 2 × 2 × 2 × 3 × 3 = 72

Final answer:

HCF = 12

LCM = 72

6. When Do We Use HCF and LCM in Real Life?

HCF and LCM help us solve everyday problems.

HCF example:

A teacher has 12 pencils and 18 erasers. She wants to make the greatest possible number of identical sets without anything left over.

HCF of 12 and 18 = 6.

She can make 6 identical sets.

LCM example:

Two school bells ring at different intervals. One rings every 4 minutes and the other every 6 minutes. If they ring together now, when will they ring together again?

LCM of 4 and 6 = 12.

They will ring together again after 12 minutes.

7. Common Mistakes Students Should Avoid

  1. Remember that HCF means the greatest common factor, not the smallest.
  2. Remember that LCM means the smallest common multiple.
  3. Do not include prime factors that are not common when calculating HCF.
  4. Do not forget any prime factor when calculating LCM.
  5. Check your answer by making sure the HCF divides each number exactly and the LCM is divisible by each number.

8. HCF and LCM Practice Questions for Grade 6

Try these questions yourself before checking the answers.

  1. Find the HCF of 8 and 12.
  2. Find the LCM of 3 and 5.
  3. Find the HCF of 15 and 25.
  4. Find the LCM of 6 and 8.
  5. Find the HCF and LCM of 12 and 20.
  6. Find the HCF and LCM of 16 and 24.
  7. Find the LCM of 5 and 10.
  8. Find the HCF of 18 and 27.

Answers

  1. HCF = 4
  2. LCM = 15
  3. HCF = 5
  4. LCM = 24
  5. HCF = 4, LCM = 60
  6. HCF = 8, LCM = 48
  7. LCM = 10
  8. HCF = 9

9. Frequently Asked Questions

Q1. What does HCF stand for?

HCF stands for Highest Common Factor. It is the greatest factor shared by two or more numbers.

Q2. What does LCM stand for?

LCM stands for Lowest Common Multiple. It is the smallest multiple shared by two or more numbers.

Q3. Which method can we use to find HCF and LCM?

We can use listing factors and multiples, prime factorization, or other methods taught in class.

Q4. Can HCF be greater than the smallest number?

No. The HCF cannot be greater than the smallest number.

Q5. Can LCM be smaller than the largest number?

No. The LCM cannot be smaller than the largest number.

Conclusion

HCF and LCM become easy when you understand their meanings and practise regularly. Remember that HCF is about common factors, while LCM is about common multiples.

Start with small numbers, practise prime factorization, and gradually try more difficult questions.

Want more Grade 6 Maths practice?

Explore the Free Grade 6 Maths Worksheets and practise more questions.

You can also improve your skills with our HCF & LCM Practice Pack at SmartStudyNest.

Learn • Practise • Grow!