Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.

Worksheet on H.C.F. and L.C.M. with Answers

Q: 1.What is HCF?

Answer: HCF ( Highest Common Factor ) is the greatest number that divides two or more numbers exactly without leaving a remainder. It is also known as the Greatest Common Factor (GCF).

Q: 2. What is LCM?

Answer: LCM ( Least Common Multiple ) is the smallest positive number that is a common multiple of two or more numbers. It is useful for solving problems involving fractions, schedules, and repeated events.

This worksheet on HCF and LCM helps students practice finding the Highest Common Factor (HCF) and Least Common Multiple (LCM) using different methods such as prime factorization, complete factorization, and long division. The worksheet includes fill-in-the-blanks, multiple practice questions, and real-life word problems with answers.

HCF and LCM are important topics in elementary mathematics because they help students solve problems involving factors, multiples, fractions, grouping, sharing, and number patterns. Regular practice builds confidence and improves problem-solving skills.

This printable worksheet is suitable for Grade 5, and Grade 6 students, teachers, homeschooling families, and parents looking for extra practice.

Note:

GCF (Greatest Common Factor)
GCD (Greatest Common Divisor)
LCD (Lowest Common Denominator)

We will solve different types of problems given in the Worksheet on H.C.F. and L.C.M.

Play Quiz

Play Game

PDF Worksheet

HCF and LCM Calculator:

Interactive HCF & LCM Visual Explanation

Worksheet for Practice:

I. Fill in the blanks:

(i) The HCF of two numbers is 1, they are called ……………. numbers.

(ii) The LCM of two or more numbers cannot be ……………. than any one of the numbers.

(iii) The HCF of the given numbers cannot be ……………. than the number themselves.

(iv) The HCF of 7 and 35 is …………….

(v) The LCM of 7 and 35 is …………….

II. Find highest common factor of the following by complete factorisation:

(i) 48, 56, 72

(ii) 198, 360

(iii) 102, 68, 136

(iv) 1024, 576

(v) 405, 783, 513

III. Find the H.C.F. by long division method:

(i) 84, 144

(ii) 120, 168

(iii) 430, 516, 817

(iv) 632, 790, 869

(v) 291, 582, 776

(vi) 219, 1321, 2320, 8526

IV. Find lowest common multiple of the following numbers:

(i) 16, 24, 40

(ii) 40, 56, 60

(iii) 207, 138

(iv) 72, 96, 120

(v) 120, 150, 135

(vi) 102, 170, 136

V. The LCM of two numbers is 60. If the product of the two numbers is 180, find their HCF.

VI. The HCF of two numbers is 40. If the product of the two numbers is 52800, find their LCM.

VII. The HCF and LCM of two numbers is 5 and 30 respectively. If one of the numbers is 10, find the other number.

Note: LCM × HCF = Product of numbers

Answers for the highest common factor (H.C.F.) and lowest common multiple (L.C.M.) are given below.

Answers:

I. (i) Co-prime

(ii) less

(iii) greater

(iv) 7

(v) 35

II. (i) 8

(ii) 18

(iii) 34

(iv) 64

(v) 27

III. (i) 12

(ii) 24

(iii) 43

(iv) 79

(v) 97

(vi) 1

IV. (i) 240

(ii) 840

(iii) 414

(iv) 1440

(v) 5400

(vi) 2040

V. 3

VI. 1320

VII. 15

Play Drag & Drop Game on HCF and LCM:

HCF & LCM Drag & Drop Game

HCF & LCM Drag & Drop

Pick up the right answer, drop it in place, and become a factor champion.

Match the answer

Solve 10 fresh HCF and LCM challenges. Drag the right answer card into the answer zone—or on touch devices, tap a card and then tap the zone.

1. Solve itFind the HCF or LCM.

2. Drag or tapMove the matching answer.

3. Score starsBuild your final medal score.

Timer (30 seconds)

Challenge 1 of 100%

0:30

Score: 0 ★

HCF

Drag the correct answer into the box below. You may also tap an answer, then tap the box.

Drop the correct answer here

Great work!

You scored 0 out of 10

Review your answers

#	Challenge	Your answer	Correct answer	Explanation

Play HCF and LCM Quiz:

HCF & LCM Challenge | Interactive Quiz

HCF & LCM Challenge

Sharpen your number skills — ten questions, one brilliant score.

Ready to play?

Each new game has 10 fresh multiple-choice questions on Highest Common Factor (HCF) and Lowest Common Multiple (LCM).

10new questions

★ 1 pointfor every correct answer

Hintsin the final review

Timer (30 seconds)

Question 1 of 100%

0:30

Score: 0 ★

HCF

Excellent work!

You scored 0 out of 10

Review your answers

#	Question	Your answer	Correct answer	Explanation

Download Printable HCF and LCM Worksheet PDF:

Grade 5 Highest Common Factor and Lowest Common Multiple practice problems with answers

FREE Printable PDF Download

After completing this worksheet students will be able to:

Frequently Asked Questions on HCF and LCM:

1.What is HCF?

Answer:

HCF (Highest Common Factor) is the greatest number that divides two or more numbers exactly without leaving a remainder. It is also known as the Greatest Common Factor (GCF).

2. What is LCM?

Answer:

LCM (Least Common Multiple) is the smallest positive number that is a common multiple of two or more numbers. It is useful for solving problems involving fractions, schedules, and repeated events.

3. What is the difference between HCF and LCM?

Answer:

The HCF is the largest common factor of two or more numbers, while the LCM is the smallest common multiple. HCF is used when dividing or grouping, whereas LCM is used when finding a common multiple.

4. How do you find HCF by prime factorization?

Answer:

Write each number as a product of its prime factors. Multiply the common prime factors with the smallest powers to get the HCF.

5. How do you find LCM using the division method?

Answer:

Write the given numbers together and divide them by common prime numbers until all the numbers become 1. Multiply all the divisors used to obtain the LCM.

6. What is the formula relating HCF and LCM?

Answer:

For any two numbers:

HCF × LCM = Product of the two numbers

This formula can be used to find either the HCF or the LCM when the other values are known.

7. Who can use this HCF and LCM worksheet?

Answer:

This worksheet is suitable for Grade 5 and Grade 6 students, teachers, parents, tutors, and homeschool learners who want extra practice with HCF and LCM concepts.

8. Does this HCF and LCM worksheet include answers?

Answer:

Yes. This worksheet includes a complete answer key so students can check their work, correct mistakes, and improve their understanding.

This worksheet has been prepared and reviewed by experienced mathematics educators to support school learning and independent practice.

About Author

Priyanka Ghosh, Founder of Math Only Math

Written by Priyanka Ghosh
Mathematics Educator | Founder of Math Only Math

Priyanka Ghosh has been teaching elementary and middle-school mathematics for over 12 years and specializes in creating simple, child-friendly math lessons and worksheets.