How to find the HCF and LCM

How to find the HCF and LCM

Understanding HCF and LCM

The Highest Common Factor (HCF) of two or more numbers is the greatest factor that all the numbers share. It’s the largest number that can exactly divide each of the numbers.
The Lowest Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the numbers. It’s the smallest number that can be divided exactly by each of the numbers.

Finding the HCF

To find the HCF of two or more numbers, first list all the factors of each number.
Then identify the common factors, which are the factors that each of the numbers share.
The highest of these common factors is the HCF.

Finding the LCM

To find the LCM of two or more numbers, first list the multiples of each number.
Then identify the common multiples shared by each of the numbers.
The smallest of these common multiples is the LCM.

Using Prime Factors to Find the HCF and LCM

Another way to find the HCF and LCM is by using prime factorisation.
Write each number as the product of its prime factors.
To find the HCF, take the lowest power of each common prime factor and multiply them.
To find the LCM, take the highest power of each prime factor (whether it’s common or not) and multiply them.

Real-life Applications of HCF and LCM

The HCF and LCM are not just abstract calculations. They have practical applications in everyday life, such as splitting things into smaller, equal parts (HCF) or finding a common multiple for different sized groups (LCM).

Common Mistakes to Avoid

Not listing all the factors or multiples of all the numbers when trying to find the HCF or LCM.
Forgetting to include the number 1 as a factor.
Mixing up the methods for finding the HCF and LCM, especially when using prime factors.
Not identifying the correct common factors or multiples for the set of numbers.