Common factors and common multiples
Choose a greatest common factor or least common multiple according to the problem.
Before you begin
- Multiplication facts
- Divisibility and prime numbers
Use common factors to share into equal groups
A factor divides a whole number with no remainder. List factor pairs or use prime factorisation to find factors shared by two numbers. The greatest common factor is useful when making the largest possible number of identical groups using everything. It also lets you factor a sum: 18 + 30 = 6(3 + 5). Expanding the bracket checks the result.
Use common multiples to find when patterns meet
A multiple is the result of multiplying by a whole number. The least positive common multiple is the first positive number appearing in both multiple lists. It is useful for repeating events and for finding common denominators. Do not automatically multiply the original numbers: their product is a common multiple but may not be the least one.
Worked example
Make the greatest possible number of identical packs from 24 pencils and 36 erasers, using all of them.
Show the worked solution
- The common factors of 24 and 36 are 1, 2, 3, 4, 6 and 12.
- The greatest is 12, so make twelve identical packs.
- Each pack receives 24 ÷ 12 = 2 pencils and 36 ÷ 12 = 3 erasers.
12 packs, each with 2 pencils and 3 erasers.
Try it yourself
Two lights flash every 6 s and 8 s, starting together. When do they next flash together?
Common mistakes
- A factor divides a number; a multiple is produced from it.
- Use the context to choose GCF or LCM.
What can you explain now?
Factor 42 + 30 using the greatest common factor. Also find the least common multiple of 9 and 12.
Compare with the explanation
6(7 + 5); LCM = 36.
The greatest common factor of 42 and 30 is 6. The positive multiples of 9 are 9, 18, 27, 36; 36 is also a multiple of 12.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Bring the ideas together
Whole numbers and decimals
Try the unit reviewOriginal StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗