Year 8: Highest common factor and lowest common multiple

What are they?

Highest Common Factor (HCF): The biggest number that divides evenly into two or more numbers. Think of it as the biggest number they both share.

Lowest Common Multiple (LCM): The smallest number that two or more numbers can both be divided into evenly. It's the smallest number that all the numbers divide into without a remainder.

Finding the HCF

• Prime Factorisation: Break each number into its prime factors. Then, take the lowest power of each prime factor that appears in all the factorisations. Multiply these lowest powers together.
• Listing Factors: List all the factors of each number. The highest factor they have in common is the HCF.

Example: HCF of 12 and 18

12 = 2² x 3

18 = 2 x 3²

The lowest power of 2 is 2¹, and the lowest power of 3 is 3¹. So, HCF(12, 18) = 2 x 3 = 6.

Finding the LCM

• Prime Factorisation: Break each number into its prime factors.
• Take the highest power of each prime factor that appears in any of the factorisations. Multiply these highest powers together.

Example: LCM of 12 and 18

12 = 2² x 3

18 = 2 x 3²

The highest power of 2 is 2², and the highest power of 3 is 3². So, LCM(12, 18) = 2² x 3² = 4 x 9 = 36.

Remember: HCF x LCM = (Product of the numbers).