LCM & HCF – Complete Concept Guide
Sainik School Entrance Examination | Full Notes + Examples + Video Classes
1️⃣ Least Common Multiple (LCM)
Definition: LCM of two or more numbers is the smallest number that is divisible by all the given numbers.
Example:
LCM(2,3) = 6
LCM(4,6,8) = 24
LCM = Product of highest powers of prime factors
2️⃣ Highest Common Factor (HCF)
Definition: HCF of two or more numbers is the greatest number that divides all the numbers exactly.
Example:
HCF(12,18) = 6
HCF(16,24) = 8
HCF = Product of lowest powers of prime factors
3️⃣ Important Relation
LCM × HCF = Product of two numbers
If LCM = 60 and HCF = 3
Product = 60 × 3 = 180
Possible numbers: 9 and 20
4️⃣ Solved Examples
Example 1: 12 and 20
- LCM = 60
- HCF = 4
Example 2: 15 and 25
- LCM = 75
- HCF = 5
Example 3: 36 and 48
- LCM = 144
- HCF = 12
5️⃣ Quick Exam Tricks 🎯
✔ Use Prime Factorization for accuracy
✔ Use LCM × HCF relation for reverse problems
✔ Practice divisibility rules
✔ Learn multiplication tables till 20
