🌟 QUICK NOTES
🔹 What is the Relation?
For two numbers:
👉 HCF × LCM = Product of the numbers
🔹 Formula
HCF×LCM=Product of the two numbers\text{HCF} \times \text{LCM} = \text{Product of the two numbers}HCF×LCM=Product of the two numbers
🔹 Example 1
Numbers = 6 and 8
- HCF = 2
- LCM = 24
👉 Check:
2 × 24 = 48
6 × 8 = 48 ✔
🔹 Example 2
Numbers = 12 and 18
- HCF = 6
- LCM = 36
👉 6 × 36 = 216
12 × 18 = 216 ✔
🔹 Important Points
- This relation is valid only for two numbers
- Helps to:
- Find LCM if HCF is known
- Find HCF if LCM is known
- Saves time in exams
📝 WORKSHEET – RELATION BETWEEN HCF & LCM
🔹 SECTION A (Basic)
- Find LCM if HCF = 2 and numbers are 4 and 6
- Check relation for numbers 5 and 10
- Check relation for numbers 3 and 7
- If HCF = 3 and numbers are 6 and 9, find LCM
- If HCF = 5 and numbers are 10 and 15, find LCM
🔹 SECTION B (Find Missing Value)
- HCF = 4, numbers = 8 and 12 → find LCM
- HCF = 6, numbers = 12 and 18 → find LCM
- HCF = 3, numbers = 9 and 15 → find LCM
- HCF = 2, numbers = 6 and 8 → find LCM
- HCF = 7, numbers = 14 and 21 → find LCM
🔹 SECTION C (Find HCF using Relation)
- LCM = 24, numbers = 6 and 8 → find HCF
- LCM = 36, numbers = 12 and 18 → find HCF
- LCM = 20, numbers = 4 and 5 → find HCF
- LCM = 42, numbers = 6 and 7 → find HCF
- LCM = 60, numbers = 12 and 15 → find HCF
🔹 SECTION D (Check True or False)
- HCF × LCM is always equal to product of numbers
- Relation works for three numbers
- LCM is always greater than HCF
- HCF can be greater than LCM
- For co-prime numbers, HCF = 1
🔥 SECTION E – CASE-BASED QUESTIONS
📖 Case Study 1
Two numbers are 8 and 12.
- Find HCF
- Find LCM
- Verify relation
📖 Case Study 2
Two numbers have product = 72 and HCF = 6.
- Find LCM
📖 Case Study 3
Two numbers are 9 and 10.
- Find HCF
- Find LCM
- Verify relation
📖 Case Study 4
Two numbers have HCF = 1 and product = 35.
- Find LCM
- What type of numbers are these?
📖 Case Study 5
- Two numbers have LCM = 60 and HCF = 5
👉 Find product of numbers
✅ ANSWER KEY
SECTION A
- 12
- 5×10=50, HCF=5, LCM=10 ✔
- 3×7=21, HCF=1, LCM=21 ✔
- 18
- 30
SECTION B
- 24
- 36
- 45
- 24
- 42
SECTION C
- 2
- 6
- 1
- 1
- 3
SECTION D
- True
- False
- True
- False
- True
SECTION E
- 4
- 24
- 4×24=96 ✔
- 12
- 1
- 90
- 1×90=90 ✔
- 35
- Co-prime
- 300