Currently Empty: $0.00
Multiples and LCM ( Least Common Multiple)
Year 8 • Number
Lesson: Multiples and LCM
Understand multiples and least common multiple (LCM) with clear explanations, examples, and practice questions – perfect for Year 8 students.
Lesson Objectives
- Understand what multiples are and list them.
- Find the LCM of two or more numbers.
- Use prime factorization to find LCM efficiently.
- Apply LCM to solve real-life word problems.
1. What Are Multiples?
A multiple of a number is the result of multiplying it by whole numbers (1, 2, 3, 4, …).
Examples
- Multiples of 4 → 4, 8, 12, 16, 20, 24, 28, …
- Multiples of 7 → 7, 14, 21, 28, 35, 42, …
Common Multiples
Common multiples are numbers that appear in the multiple lists of two or more numbers.
Common multiples are numbers that appear in the multiple lists of two or more numbers.
Multiples of 4 → 4, 8, 12, 16, 20, 24, 28
Multiples of 6 → 6, 12, 18, 24, 30
Common multiples → 12, 24, … (smallest is 12)
2. What is LCM?
LCM stands for Least Common Multiple. It is the
smallest multiple that two or more numbers share.
Example 1
Find the LCM of 5 and 6.
- Multiples of 5 → 5, 10, 15, 20, 25, 30
- Multiples of 6 → 6, 12, 18, 24, 30
- Common multiples → 30, 60, …
LCM = 30
3. LCM Using Prime Factorization (Fast Method)
Steps:
- Write prime factorization of each number.
- Take the highest power of each prime.
- Multiply them to get the LCM.
Example 2
Find the LCM of 12 and 18.
- 12 = 2² × 3
- 18 = 2 × 3²
Take highest powers: 2² and 3²
LCM = 2² × 3² = 36
4. Real-Life Example
A bell rings every 8 minutes, another bell rings every 12 minutes.
After how many minutes will both ring together?
Find LCM(8, 12):
8 = 2³
12 = 2² × 3
LCM = 2³ × 3 = 24 minutes
Practice Questions
A. Find the first 5 multiples
- First 5 multiples of 9
- First 5 multiples of 7
B. Find the LCM
- LCM of 4 and 6
- LCM of 8 and 20
- LCM of 10 and 15
C. Using Prime Factorization
- LCM of 18 and 24
- LCM of 14 and 35
- LCM of 16, 20, and 24
D. Word Problems
- Two traffic lights change after 30 seconds and 45 seconds. After how many seconds will they change together?
- A man jogs every 12 days, and his friend jogs every 18 days. After how many days will they jog together again?
✅ Show Answer Key
A. Multiples
- Multiples of 9 → 9, 18, 27, 36, 45
- Multiples of 7 → 7, 14, 21, 28, 35
B. LCM
- LCM(4, 6) = 12
- LCM(8, 20) = 40
- LCM(10, 15) = 30
C. Prime Factorization
- LCM(18, 24) = 72
- LCM(14, 35) = 70
- LCM(16, 20, 24) = 240
D. Word Problems
- LCM(30, 45) = 90 seconds
- LCM(12, 18) = 36 days
© Aviate Learning – Multiples & LCM (Year 8)