Finding Common Ground

Overview

This chapter explores factors and multiples shared by numbers. We find common factors, the HCF, common multiples and the LCM, useful for simplifying and combining quantities.

Key concepts

• Factors divide a number exactly; multiples are products of a number.
• Common factors and the Highest Common Factor (HCF).
• Common multiples and the Lowest Common Multiple (LCM).
• Prime factorisation helps find HCF and LCM.

Important formulae

• HCF = product of common prime factors
• LCM = product of all prime factors with highest powers
• HCF × LCM = product of the two numbers

Solved example

1. Find the HCF of 12 and 18.
2. 12 = 2 × 2 × 3; 18 = 2 × 3 × 3.
3. Common factors: 2 × 3 = 6, so HCF = 6.

Important questions

1. Find the LCM of 4 and 6.
2. List the common factors of 16 and 24.
3. Find HCF and LCM of 9 and 15, and verify HCF × LCM = 9 × 15.
4. Is 1 a common factor of every pair of numbers?

Quick revision

HCF is the largest shared factor; LCM is the smallest shared multiple. Use prime factorisation, and remember HCF × LCM equals the product of the two numbers.