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.
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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
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.