Discover
Buses leave every 4 minutes and trains every 6 minutes. Both leave now. When do they next leave together?
- In 12 minutes
- In 2 minutes
Key idea
GCF splits into equal groups; LCM lines things up.
The greatest common factor (GCF) is the largest number that divides both numbers. The least common multiple (LCM) is the smallest number that both divide. Example: GCF(12, 18) = 6, LCM(12, 18) = 36.
Worked example
12 and 20.
GCF = 4
Factors in common: 1, 2, 4.
LCM = 60
Multiples of 20: 20, 40, 60.
Your turn, guided
Your turn: the GCF of 18 and 24.
Largest common factor.
Practice ★
- What is the greatest common factor of 12 and 30?
- What is the greatest common factor of 20 and 28?
- Juice boxes come in packs of 5 and straws in packs of 7. What is the smallest number of each you can buy so that the numbers match?
Watch out!
Practice ★★
- What is the least common multiple of 18 and 30?
- What is the least common multiple of 9 and 15?
Exit ticket
Three questions to check you have got it.
- What is the greatest common factor of 12 and 30?
- What is the greatest common factor of 20 and 28?
- What is the greatest common factor of 14 and 10?
Summary card
Common factors and multiples
GCF: largest common divisor. LCM: smallest common multiple.
Watch out: do not swap them.