HCF and LCM
Practise finding the highest common factor (HCF), sometimes called the greatest common divisor, and the lowest common multiple (LCM) of two numbers.
This is level 1; Finding the highest common factor (HCF) of two numbers. You can earn a trophy if you get at least 9 correct and you do this activity online.
Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.
When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.
Please contact me if you have any suggestions or questions.
Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?
Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:
"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"
Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School:
"Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work."
There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.
A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.
Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.
If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:Subscribe
Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.
Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.
If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
© Transum Mathematics :: This activity can be found online at:
Level 1 - Finding the highest common factor (HCF) of two numbers.
Level 2 - Finding the lowest common multiple (LCM) of two numbers
Level 3 - Finding the highest common factor (HCF) of large numbers.
Level 4 - Finding the lowest common multiple (LCM) of large numbers
Level 5 - Finding the HCF and LCM of three numbers
Sieve Use the Sieve of Eratosthenes to find prime numbers.
Factor Trees An interactive and very visual way to break down a number into its prime factors.
The highest common factor (HCF) of two numbers is the largest number that divides exactly into both of the numbers.
You can Find the HCF of
numbers by listing the prime factors of both numbers then multiplying together the factors that appear in both lists.
A Venn diagram may help you with this task.
e.g., Find the HCF of
24 and 36
24 = 2x2x2x3 and 36 = 2x2x3x3
so the HCF of 24 and 36 is 2x2x3 = 12
The lowest common multiple (LCM), or least common multiple, is the smallest number that both numbers divide into exactly.
You can Find the LCM of
numbers by listing the prime factors of both numbers and then multiply all the prime factors of the larger number by those prime factors of the smaller number that are not already included.
e.g., Find the LCM of
24 and 36
24 = 2x2x2x3 and 36 = 2x2x3x3
so the LCM of 24 and 36 is 2x2x3x3 x 2 = 72
Click here to see an animated demonstration of this cool way to find both the HCF and LCM of two numbers.
When you have found the HCF of the numbers a and b the LCM can be found using the following formula:
It is worth knowing that HCF is also known as GCD. If you are using a spreadsheet such as Excel there are functions named LCM and GCD for calculating the LCM and HCF.
Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.