What is LCF & HCF ? Tricks
1. HCF (Highest Common Factor), Also called: GCD (Greatest Common Divisor)
Definition: HCF is the greatest number that divides two or more given numbers exactly. HCF āĻŦā§āĻ˛āĻŋāĻ˛ā§ āĻĻā§āĻāĻž āĻŦāĻž āĻ¤āĻ¤ā§āĻ§āĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻžāĻ āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖāĻāĻžā§ąā§ āĻāĻžāĻ āĻā§°āĻŋāĻŦ āĻĒā§°āĻž āĻ¸ā§°ā§āĻŦāĻžāĻ§āĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻžāĻ āĻŦā§āĻāĻžāĻ¯āĻŧāĨ¤
Ex / āĻāĻĻāĻžāĻšā§°āĻŖ: Find HCF of 12 and 18.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 2, 3, 6
HCF = 6
2. LCM (Least Common Multiple)
Definition: LCM is the smallest number that is a multiple of two or more given numbers. LCM āĻŦā§āĻ˛āĻŋāĻ˛ā§ āĻĻā§āĻāĻž āĻŦāĻž āĻ¤āĻ¤ā§āĻ§āĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻ¸ā§°ā§āĻŦāĻ¨āĻŋāĻŽā§āĻ¨ āĻ¸āĻžāĻ§āĻžā§°āĻŖ āĻā§āĻŖāĻŋāĻ¤āĻāĻ āĻŦā§āĻāĻžāĻ¯āĻŧāĨ¤
Ex / āĻāĻĻāĻžāĻšā§°āĻŖ: Find LCM of 12 and 18.
Write prime factors
12 = 2 × 2 × 3 = 2²×3
18 = 2 × 3 × 3 = 2×3²
Highest power of each prime: 2², 3²
LCM = 36
Key Difference
- HCF: Biggest common divisor. HCF: āĻ¸ā§°ā§āĻŦāĻžāĻ§āĻŋāĻ āĻ¸āĻžāĻ§āĻžā§°āĻŖ āĻā§āĻŖāĻ¨ā§āĻ¯āĻŧāĻ
- LCM: Smallest common multiple. LCM: āĻ¸ā§°ā§āĻŦāĻ¨āĻŋāĻŽā§āĻ¨ āĻ¸āĻžāĻ§āĻžā§°āĻŖ āĻā§āĻŖāĻŋāĻ¤āĻ
What is LCF & HCF ? Tricks