Prime factors, HCF and LCM – Year 9 maths lesson
Lesson 1 of 38 in the Year 9 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 9 (ages 13–14) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 9 (ages 13–14)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why is the LCM of two numbers never smaller than either number?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Mixing up factors and multiples. Factors fit into the number; multiples come out of it.
- Stopping a factor tree at a number that is not prime. Keep splitting until every end is prime.
Tip for home: Work out when two events that repeat (buses, reminders) will next happen together.
What your child will learn
We are learning to write numbers as products of prime factors and find the highest common factor and lowest common multiple.
Success looks like
- I can write a number as a product of primes.
- I can find the HCF.
- I can find the LCM.
Key words
- prime
- a number with exactly two factors
- factor
- a number that divides exactly
- multiple
- a number in the times table
- product
- the result of multiplying
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Build factor trees for two numbers, then sort the primes into a Venn diagram.
The big ideas (for the adult)
Every whole number above 1 can be written as a product of primes: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5. A factor tree finds them.
The highest common factor (HCF) is the biggest number that divides both. Use the primes they share.
The lowest common multiple (LCM) is the smallest number both divide into. A Venn diagram of prime factors helps with both.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 9 maths lessons
- Rounding and estimation
- Bounds and error intervals
- Standard form
- Laws of indices
- Powers and roots
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Angle facts and parallel lines
- Angles in polygons
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Quadrilaterals and symmetry
- Coordinate geometry
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Pie charts and time series graphs
- Sampling
- Relative frequency and expected outcomes
- Venn diagrams and conditional probability
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Inequalities
- Rearranging formulae
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- Percentages
- Speed, density and pressure
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 9: “use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property”
GCSE subject content N4: “use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.