# LCM and HCF

## 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.