HCF and LCM Applications

Discover the mathematical ballet of prime factors! Learn to find HCF (weakest links) and LCM (strongest chains) using the power of prime factorization.

Welcome to HCF and LCM!

Let's discover how prime factorization helps us find
the greatest common divisor and least common multiple

6
6 = 2¹ × 3¹
20
20 = 2² × 5¹

Finding HCF of 6 and 20

Common factors: 2
Smallest power: 2¹
HCF = 2

Finding LCM of 6 and 20

All factors: 2², 3¹, 5¹
Greatest powers: 2² × 3¹ × 5¹
LCM = 60
⚖️ Mathematical Balance
HCF × LCM = 2 × 60 = 120
⚖️
a × b = 6 × 20 = 120
✅ Perfect Balance Achieved!
96
96 = 2⁵ × 3¹
404
404 = 2² × 101¹

HCF and LCM of 96 and 404

HCF = 2² = 4
LCM = (96 × 404) ÷ 4 = 9696
Verification: 4 × 9696 = 38784 = 96 × 404 ✅

Three Numbers: 6, 72, 120

6
2¹ × 3¹
72
2³ × 3²
120
2³ × 3¹ × 5¹
HCF × LCM = a × b × c ❌
Product formula doesn't work for 3+ numbers!

HCF and LCM of 6, 72, 120

HCF = 2¹ × 3¹ = 6
LCM = 2³ × 3² × 5¹ = 360
Method: Smallest powers for HCF, Greatest powers for LCM
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🎯 Mathematical Insights
HCF and LCM are fundamental tools in mathematics. HCF finds the greatest common divisor (weakest link), while LCM finds the least common multiple (strongest chain). Select a demonstration above to explore these powerful concepts!