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 6: Mixed application questions. 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 23 September 'Starter of the Day' page by Judy, Chatsmore CHS: "This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles." Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk: "Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!" 
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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
Level 6  Mixed application questions
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.
Advanced calculators have built in functions for finding the HCF and LCM of two numbers but there is a trick for finding the HCF using a modern scientific calculator.
If the two numbers are entered using the fraction template the calculator will express that fraction in its lowest terms. It does this by dividing numerator and denominator by their HCF.
For example to find the HCF of 24 and 36 enter 24/36 then press enter.
Considering the denominators, we now need to find what 24 was divided by to give 2. So dividing 24 by 2 gives 12 which is the HCF.
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.
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