🎯 Learning Objectives
- Factorise algebraic terms and expressions.
- Find the highest common factor (HCF).
- Find the lowest common multiple (LCM).
Introduction
This lesson develops HCF and LCM of Algebraic Expressions from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
🤔 Start with an Idea
Think of the HCF as the largest complete building block shared by every expression. The LCM is the smallest expression that contains every required factor.
📖 Key Notes
Write each term as a product of numerical and variable factors. For the HCF, choose common factors with the smallest powers. For the LCM, choose all factors with the largest powers.
18xy² = 2 × 3² × x × y²
🧩 Factor Match
Find the factors present in both expressions.
🧠 Let's Think Together
Question: Find the HCF of 12x²y and 18xy².
- Which numerical factors are common? 2 and 3.
- What is the smallest power of x present? x¹.
- What is the smallest power of y present? y¹.
✍️ Worked Examples
🎯 Practice Questions
Easy
Find the HCF of 10x and 15x².
Show answer
5x
Medium
Find the LCM of 8a²b and 12ab³.
Show answer
24a²b³
⚠️ Common Mistakes
- Using the largest powers for an HCF.
- Forgetting numerical prime factors.
- Finding the HCF of terms before fully factorising them.
📝 Exam Focus
Show factorisation clearly. Marks are often awarded for a correct factor breakdown even when the final answer is wrong.
Summary
- HCF: common factors, smallest powers.
- LCM: every required factor, largest powers.
- Factorise first.