Class 8 Maths – Chapter 16: Playing with Numbers
Step 9: Finding Two Numbers using LCM and HCF
Sometimes, the LCM and HCF of two numbers are given. Using this information, we can find the numbers.
🔹 Key Formula
LCM × HCF = Product of the two numbers
📘 Example 1
Find the two numbers if their HCF = 6 and LCM = 72.
Solution:
Product of the numbers = 6 × 72 = 432
Let the numbers be 6 × x and 6 × y (where x and y are co-prime)
x × y = 432 ÷ 36 = 12
Possible co-prime factors of 12 are: 3 and 4
Hence, the required numbers are: 6 × 3 = 18 and 6 × 4 = 24
📘 Example 2
Find the numbers if HCF = 5 and LCM = 150.
Product = 5 × 150 = 750
Let numbers = 5x and 5y
x × y = 750 ÷ 25 = 30
Co-prime factors of 30 → 5 and 6
Numbers = 25 and 30
📝 Exam Writing Steps
- Write the formula
- Find the product
- Express numbers as HCF × co-prime numbers
- Find suitable co-prime factors
- Write the final answer clearly
🧠 Easy Memory Trick
HCF outside ✖️
Co-prime inside 🔢
Multiply → Get numbers ✅
📘 Class 8 Mathematics – Complete Library
CBSE | NCERT | State Syllabus
Chapter 1: Rational Numbers
Chapter 2: Linear Equations in One Variable
Chapter 3: Understanding Quadrilaterals
Chapter 4: Practical Geometry
Chapter 5: Data Handling
Chapter 6: Squares and Square Roots
Chapter 7: Cubes and Cube Roots
- NCERT Notes
- MCQs
- Worksheet
- Worksheet Answers
- Mind Map & Easy Tricks
- Important Exam Questions
- Very Important Questions
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