Practice HCF & LCM Concept with Notes & Mock Test

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.

💡 Shortcut Trick:

1. Use the division method:
2. Divide the larger number by the smaller number.
3. Take the remainder and divide the previous divisor.
4. Repeat until the remainder is 0.
5. 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.

🔥 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 ✅

🎯 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! 😊

📜 Quiz Instructions

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• ⏳ Each question has 60 seconds to answer.
• 🎯 Each question carries 10 marks.
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