LCM and HCF

LCM (Least Common Multiple): • Smallest number divisible by all given numbers • Method 1: List multiples, find common smallest • Method 2: Prime factorization • Example: LCM of 12 and 18 12 = 2² × 3, 18 = 2 × 3² LCM = 2² × 3² = 4 × 9 = 36

HCF (Highest Common Factor): • Largest number that divides all given numbers • Also called GCD (Greatest Common Divisor) • Method 1: List factors, find common largest • Method 2: Prime factorization • Example: HCF of 12 and 18 12 = 2² × 3, 18 = 2 × 3² HCF = 2 × 3 = 6

Relationship: LCM × HCF = Product of two numbers