🌟 QUICK NOTES (MULTIPLES)
🔹 What are Multiples?
Multiples are numbers obtained by multiplying a number by natural numbers (1, 2, 3, …)
👉 Example:
Multiples of 4 → 4, 8, 12, 16, 20…
🔹 Key Properties
- Multiples are infinite
- Multiples are always greater than or equal to the number
- Every number is a multiple of itself
- Multiples increase in a pattern
🔹 Common Multiples
Multiples common to two numbers
👉 Example:
Multiples of 3 → 3, 6, 9, 12…
Multiples of 4 → 4, 8, 12…
👉 Common → 12, 24, 36…
📝 EXERCISE 3.2 WORKSHEET (MULTIPLES)
🔹 SECTION A (Very Short Answer)
- Write first 5 multiples of 3.
- Write first 5 multiples of 7.
- Write first 5 multiples of 10.
- What is the smallest multiple of any number?
- Is every number a multiple of itself?
- Write first 3 multiples of 12.
- Write first 5 multiples of 5.
- Write first 4 multiples of 9.
- Write first 5 multiples of 2.
- Are multiples finite or infinite?
🔹 SECTION B (Short Answer)
- Write first 6 multiples of 4.
- Write first 6 multiples of 6.
- Write first 5 multiples of 8.
- Write first 5 multiples of 15.
- Write first 5 multiples of 11.
- Write first 5 multiples of 20.
- Write first 5 multiples of 25.
- Write first 6 multiples of 9.
- Write first 5 multiples of 14.
- Write first 5 multiples of 18.
🔹 SECTION C (Common Multiples)
- Find first 3 common multiples of 2 and 3.
- Find first 3 common multiples of 3 and 4.
- Find first 3 common multiples of 4 and 5.
- Find first 3 common multiples of 6 and 8.
- Find first 3 common multiples of 5 and 7.
- Find first 3 common multiples of 3 and 6.
- Find first 3 common multiples of 9 and 12.
- Find first 3 common multiples of 2 and 5.
- Find first 3 common multiples of 7 and 10.
- Find first 3 common multiples of 8 and 12.
🔹 SECTION D (Concept Based)
- Which is the smallest common multiple of 3 and 5?
- Which is the smallest common multiple of 4 and 6?
- Which is the smallest common multiple of 5 and 10?
- Write the smallest common multiple of 2, 3 and 4.
- Which is the smallest common multiple of 6 and 9?
🔥 SECTION E – CASE-BASED QUESTIONS
📖 Case Study 1: School Bell
A bell rings every 3 minutes and another every 5 minutes.
- After how many minutes will both ring together first?
- Write next two times they will ring together.
📖 Case Study 2: Sports Practice
A student practices running every 4 days and cycling every 6 days.
- After how many days will both happen together?
- Write next two such days.
📖 Case Study 3: Factory Production
Machine A produces every 2 hours and Machine B every 5 hours.
- When will both produce together first?
- Write next two such times.
📖 Case Study 4: Number Pattern
Multiples of 6 → 6, 12, 18…
Multiples of 9 → 9, 18, 27…
- Write first 3 common multiples.
- Which is the smallest common multiple?
📖 Case Study 5: Puzzle
- A number is a multiple of both 4 and 5.
👉 Write smallest such number - Write next two multiples of this number
- A number is multiple of 3 but not 2
👉 Write one example - A number is multiple of 2, 3 and 5
👉 Write smallest such number - Write first 3 multiples of that number
- Write a number that is a common multiple of 6 and 8
- Is 24 a multiple of 3? Explain
✅ ANSWER KEY
SECTION A
- 3,6,9,12,15
- 7,14,21,28,35
- 10,20,30,40,50
- The number itself
- Yes
- 12,24,36
- 5,10,15,20,25
- 9,18,27,36
- 2,4,6,8,10
- Infinite
SECTION B
- 4,8,12,16,20,24
- 6,12,18,24,30,36
- 8,16,24,32,40
- 15,30,45,60,75
- 11,22,33,44,55
- 20,40,60,80,100
- 25,50,75,100,125
- 9,18,27,36,45,54
- 14,28,42,56,70
- 18,36,54,72,90
SECTION C
- 6,12,18
- 12,24,36
- 20,40,60
- 24,48,72
- 35,70,105
- 6,12,18
- 36,72,108
- 10,20,30
- 70,140,210
- 24,48,72
SECTION D
- 15
- 12
- 10
- 12
- 18
SECTION E
- 15 minutes
- 30, 45
- 12 days
- 24, 36
- 10 hours
- 20, 30
- 18, 36, 54
- 18
- 20
- 40, 60
- Example: 9
- 30
- 30, 60, 90
- Example: 24
- Yes (24 ÷ 3 = 8)