Free HCF and LCM Worksheet with Answers (Printable PDF)
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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.
HCF and LCM Calculator:
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
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Download Printable HCF and LCM Worksheet PDF:
After completing this worksheet students will be able to:
Frequently Asked Questions on HCF and LCM:
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).
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.
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.
Answer:
Write each number as a product of its prime factors. Multiply the common prime factors with the smallest powers to get the HCF.
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.
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.
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.
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
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.
Related Resources:
● Multiples.
Common Multiples.
Least Common Multiple (L.C.M).
To find Least Common Multiple by using Prime Factorization Method.
Examples to find Least Common Multiple by using Prime Factorization Method.
To Find Lowest Common Multiple by using Division Method
Examples to find Least Common Multiple of two numbers by using Division Method
Examples to find Least Common Multiple of three numbers by using Division Method
Relationship between H.C.F. and L.C.M.
Worksheet on H.C.F. and L.C.M.
Word problems on H.C.F. and L.C.M.
Worksheet on word problems on H.C.F. and L.C.M.
5th Grade Math Problems
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