🌟 QUICK NOTES (LCM)
🔹 What is LCM?
The Lowest Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers.
🔹 Method 1: Listing Multiples
✅ Example: Find LCM of 4 and 6
Multiples of 4 → 4, 8, 12, 16…
Multiples of 6 → 6, 12, 18…
👉 Common multiples → 12, 24…
👉 LCM = 12
🔹 Method 2: Prime Factorisation
✅ Example: Find LCM of 8 and 12
8 = 2³
12 = 2² × 3
👉 Take highest powers
👉 LCM = 2³ × 3 = 24
🔹 Important Points
- LCM is always ≥ greatest number
- Used in time, repetition, cycles problems
- For two numbers:
👉 LCM × HCF = Product of numbers
📝 WORKSHEET – LCM (EXERCISE 3.5)
🔹 SECTION A (Very Short Answer)
- Find LCM of 4 and 5
- Find LCM of 3 and 7
- Find LCM of 2 and 6
- Find LCM of 5 and 10
- Find LCM of 6 and 8
- What is LCM of two equal numbers?
- What is LCM of 1 and any number?
- Find LCM of 9 and 3
- Find LCM of 7 and 14
- Find LCM of 10 and 20
🔹 SECTION B (Using Multiples Method)
- Find LCM of 4 and 6
- Find LCM of 5 and 8
- Find LCM of 3 and 9
- Find LCM of 6 and 7
- Find LCM of 8 and 12
- Find LCM of 9 and 10
- Find LCM of 12 and 15
- Find LCM of 6 and 14
- Find LCM of 15 and 20
- Find LCM of 16 and 24
🔹 SECTION C (Prime Factorisation Method)
- Find LCM of 12 and 18
- Find LCM of 20 and 30
- Find LCM of 24 and 36
- Find LCM of 45 and 75
- Find LCM of 72 and 108
🔥 SECTION D – CASE-BASED QUESTIONS
📖 Case Study 1: School Bell
A bell rings every 4 minutes and another every 6 minutes.
- After how many minutes will both ring together?
- Write next two such times
📖 Case Study 2: Traffic Signals
Two signals change every 5 sec and 8 sec.
- When will both change together?
- Write next two such times
📖 Case Study 3: Sports Practice
A player runs every 6 days and swims every 9 days.
- After how many days both happen together?
- Write next two such days
📖 Case Study 4: Number Puzzle
- Find smallest number divisible by both 3 and 5
- Find smallest number divisible by 4 and 6
- Find smallest number divisible by 2, 3 and 5
📖 Case Study 5: Factory Production
Machines produce every 8 hours and 12 hours.
- When will both produce together?
- Write next two such times
🔥 SECTION E – THINKING QUESTIONS
- Can LCM be smaller than given numbers?
- Find LCM of 1 and 25
- Which is greater: LCM of (4,6) or (3,5)?
- Find two numbers whose LCM is 20
- Find two numbers whose LCM is 12
🔹 SECTION F (Mixed Practice)
- Find LCM of 6 and 9
- Find LCM of 8 and 10
- Find LCM of 12 and 16
- Find LCM of 18 and 24
- Find LCM of 20 and 25
- Find LCM of 14 and 21
- Find LCM of 9, 12 and 15
- Find LCM of 4, 6 and 8
- Find LCM of 5, 10 and 15
✅ ANSWER KEY
SECTION A
- 20
- 21
- 6
- 10
- 24
- Same number
- The number
- 9
- 14
- 20
SECTION B
- 12
- 40
- 9
- 42
- 24
- 90
- 60
- 42
- 60
- 48
SECTION C
- 36
- 60
- 72
- 225
- 216
SECTION D
- 12 minutes
- 24, 36
- 40 sec
- 80, 120
- 18 days
- 36, 54
- 15
- 12
- 30
- 24 hours
- 48, 72
SECTION E
- No
- 25
- 12 vs 15 → 15 greater
- Example: 4 and 5
- Example: 3 and 4
SECTION F
- 18
- 40
- 48
- 72
- 100
- 42
- 180
- 24
- 30