# HCF & LCM

These lessons help GCSE/IGCSE Maths students learn how to find the highest common factor (HCF) and lowest common multiple (LCM).

The following diagrams show how to find the HCF and LCM of 24 and 36 using Factor Trees and Venn Diagram. Scroll down the page for more examples.

The following diagram shows how to find the HCF and LCM of 24 and 36 using Repeated Division.

We also have a Highest Common Factor Calculator and a Least Common Multiple Calculator. Use them to check your answers.

Highest Common Factor, Lowest Common Multiple

GCSE Tutorial
Find HCF and LCM by listing, by prime factorization and by using Venn Diagrams.

Example:

1. Find the LCM and HCF of
a) 8 and 12
b) 6 and 16
c) 24 and 42
d) 72 and 84
e) 80 and 36

How To Work Out HCF And LCM Using Short Division?

Example:
Find the HCF and LCM of 108 and 24.

How To Work Out HCF And LCM Using Prime Factorization?

Watch this GCSE maths revision lesson on Highest Common Factor (HCF) and Lowest Common Multiple (LCM).

Example:

1. Express 60 as the product of its prime factors.
2. Find the HCF of 24 and 36.
3. Find the LCM of 8 and 12.

How To Find The HCF And LCM Using Prime Factor Decomposition And Venn Diagrams?

Examples:

1. Work out the highest common factor (HCF) and lowest common multiple (LCM) of 48 and 60.
2. Work out the HCF and LCM of 140 and 210.

How To Use A Venn Diagram Method To Find LCM And HCF?

Find the LCM and HCF of 24 and 60.

How To Solve LCM And HCF (GCF) Word Problems?

Example:

1. William and Luis are in different physics class at Santa Rita. Luis' teacher always gives exams with 30 questions while William’s teacher gives more frequent exams with only 24 questions. Luis' teacher also assigns 3 projects per year. Even though the two classes have to take a different number of exams, their teachers have told them that both classes will get the same total number of exam questions each year.
What is the minimum number of exam questions William’s or Luis' class can expect to get in year?
2. Umaima just bought 1 package of 21 binders. She also bought 1 package of 30 pencils. She wants to use all the binders and pencils to create identical sets of office supplies for her classmates.
What is the greatest number of identical sets Umaima can make using all the supplies?

How To Distinguish And Solve GCF (HCF) And LCM Word Problems?

Examples:

1. Sheila has 28 Skittle Bags and 36 Hershey Bars. If she wants to make goody bags with an equal amount of Skittles in each bag and an equal amount of Hershey Bars in each bag, what is the greatest number of bags she can make? How many Skittles will be in each bag? How many Hershey Bars will be in each bag?
2. Train A makes its stops in 45 minutes. Train B makes its stops in 60 minutes. How many minutes will pass before the two meet? In this time, how many loops will Train A make? How many loops will Train B make?

The following Highest Common Factor Calculator will help you find the HCF of a list of numbers.

Greatest Common Factor Calculator
(Calculator Widget Copyright CalculatorSoup, LLC at www.calculatorsoup.com.)

The following Least Common Multiple Calculator will help you find the LCM of a list of numbers.

LCM Calculator - Least Common Multiple
(Calculator Widget Copyright CalculatorSoup, LLC at www.calculatorsoup.com.)

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.