LCM and HCF (Edexcel GCSE Maths): Revision Notes
LCM and HCF
Introduction
While these mathematical terms might sound intimidating at first, LCM and HCF are actually quite straightforward concepts once you understand what they mean and how to find them.
LCM (Lowest Common Multiple)
What is LCM?
The Lowest Common Multiple is the smallest number that can be divided by all the numbers you're working with. Think of it as finding the smallest number that all your given numbers will "fit into" evenly.
Method for finding LCM
Follow these simple steps:
- List the multiples of each number you're working with
- Identify the smallest number that appears in all the lists
- That's your answer!
Example: Finding LCM of 12 and 15
Worked Example: Finding LCM of 12 and 15
Let's work through this step by step:
Looking at the multiples:
- Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96...
- Multiples of 15: 15, 30, 45, 60, 75, 90, 105...
The first number that appears in both lists is 60, so the LCM of 12 and 15 is 60.
HCF (Highest Common Factor)
What is HCF?
The Highest Common Factor is the largest number that divides evenly into all the numbers you're working with. It's the biggest number that can divide into each of your given numbers without leaving a remainder.
Method for finding HCF
The process is similar to finding LCM:
- List all the factors of each number
- Find the largest number that appears in all the lists
- That's your HCF!
Example: Finding HCF of 36, 54, and 72
Worked Example: Finding HCF of 36, 54, and 72
Let's list the factors:
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The largest number that appears in all three lists is 18, so the HCF of 36, 54, and 72 is 18.
Important tips
When listing factors, be systematic and careful to avoid missing any. It's worth double-checking your work by ensuring you haven't overlooked any factors, as this could lead to an incorrect answer.
Make sure you understand the difference between the two concepts:
- LCM: We're looking for the smallest common multiple
- HCF: We're looking for the largest common factor
Practice questions
Try these questions to test your understanding:
Q1: Find the Lowest Common Multiple (LCM) of 9 and 12.
Q2: Find the Highest Common Factor (HCF) of 36 and 84.
Remember!
Key Points to Remember:
- LCM finds the smallest number that all given numbers divide into
- HCF finds the largest number that divides into all given numbers
- For LCM, list the multiples of each number
- For HCF, list the factors of each number
- Always double-check your factor lists to avoid missing any numbers