HCF and LCMPractise 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.
InstructionsTry 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. 



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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 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je: "I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson." Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne: "Very good starters, help pupils settle very well in maths classroom." 


AnswersThere 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 adfree 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 

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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
When you have found the HCF of the numbers a and b the LCM can be found using the following formula:
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.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
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