Many students find HCF (Highest Common Factor) and LCM (Least Common Multiple) confusing, but with the right approach, these concepts become easy. Let’s break it down in a way that anyone can understand.
📌 What is HCF (Highest Common Factor)?
HCF is the largest number that divides two or more numbers completely without leaving any remainder.
👉 Example: Find the HCF of 18 and 24.
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 3, 6
- The highest among them is 6. So, HCF(18, 24) = 6.
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 3, 6
- The highest among them is 6. So, HCF(18, 24) = 6.
💡 Shortcut Trick:
- Use the division method:
- Divide the larger number by the smaller number.
- Take the remainder and divide the previous divisor.
- Repeat until the remainder is 0.
- The last divisor is the HCF.
📌 What is LCM (Least Common Multiple)?
LCM is the smallest number that is divisible by two or more given numbers.
👉 Example: Find the LCM of 12 and 15.
- Multiples of 12: 12, 24, 36, 48, 60, 72, ...
- Multiples of 15: 15, 30, 45, 60, 75, ...
- The smallest common multiple is 60. So, LCM(12, 15) = 60.
- Multiples of 12: 12, 24, 36, 48, 60, 72, ...
- Multiples of 15: 15, 30, 45, 60, 75, ...
- The smallest common multiple is 60. So, LCM(12, 15) = 60.
🔥 Quick Formula to Find HCF and LCM
For two numbers:
a × b = HCF(a, b) × LCM(a, b)
👉 Example: Given HCF(8, 12) = 4, find LCM.
a × b = HCF × LCM
8 × 12 = 4 × LCM
96 = 4 × LCM
LCM = 24 ✅
a × b = HCF × LCM
8 × 12 = 4 × LCM
96 = 4 × LCM
LCM = 24 ✅
🎯 Real-Life Uses of HCF and LCM
- HCF in real life: When dividing items equally, like distributing 18 chocolates and 24 biscuits among friends.
- LCM in real life: When finding the least time two events will coincide, like the blinking of traffic lights.
🚀 Vedic Math Trick for Faster Calculation
For LCM using the shortcut:
- Write down the numbers.
- Take the highest prime factors directly.
- Multiply without repeating common factors.
For HCF using the shortcut:
- Use the continuous division method.
- Keep dividing until the remainder is 0.
- The last divisor is the HCF.
❓ Challenge Question
Find the HCF and LCM of 20, 25, and 30 using the prime factorization method. Drop your answer in the comments! 😊
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