Greatest common factor and least common multiple – Grade 6 math lesson
Lesson 14 of 26 in the Grade 6 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 6 (ages 11–12) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 6 (ages 11–12)
- You need
- Paper, a pencil and this page
- Graded
- 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 graded straight away with a worked explanation, so you never have to grade 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
Learning goal: find the greatest common factor and the least common multiple of two numbers.
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 multiplication 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 greatest common factor (GCF) is the biggest number that divides both. Use the primes they share.
The least 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 | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded 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 graded instantly.
More practice
More Grade 6 math lessons
- Solving word problems
- Fractions, decimals and percentages
- Ratios
- One quantity as a fraction or percentage of another
- Percent
- Proportional relationships
- Rates and unit rates
- Unit prices and best buys
- Converting units
- Negative numbers and temperature
- Integers and absolute value
- Operations with multi-digit decimals
- Operations with fractions
- Square and cube numbers
- Writing expressions
- Evaluating expressions
- Simplifying expressions
- Solving equations
- Inequalities
- Writing equations for situations
- 3-D shapes and nets
- Coordinates
- Volume and surface area
- Mean, median and mode
- Box plots and interquartile range
Curriculum
Common Core State Standards 6.NS.B.4: “Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)..”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.