LCM and HCF

The Lowest Common Multiple (LCM) refers to the smallest multiple that is common to two or more numbers.
To find the LCM of two or more numbers, you may list the multiples of each number and identify the smallest common multiple.
Another method would be to prime factorise each number, then use the highest powers of these prime factors to determine the LCM.
The LCM is especially useful in solving problems that involve repeated events or cycles occurring at different intervals.
Highest Common Factor (HCF) represents the largest number that is a factor of two or more numbers.
To derive the HCF of two or more numbers, it’s necessary to list all of the factors for each number and identify the largest common factor.
An alternate and quicker method might be to use prime factorisation for each number, then use the lowest powers of these prime factors to determine the HCF.
The HCF is essential when solving problems that need a ‘greatest’ shared measurement or quantity.
Bear in mind that the HCF is always equal to or less than the smallest number, while the LCM is always equal to or greater than the largest number.
When two numbers are prime to each other (share no common factors other than 1), their HCF is 1, and their LCM is the product of the numbers.
The product of two numbers is equivalent to the product of their HCF and LCM.

Remember to practice problem-solving to help internalise these concepts. Work through past paper questions related to HCF and LCM to become more confident at identifying the necessary steps and applying the right methods.