Example 1
\(\text{GCD}(12, 18) = 6, \text{LCM}(12, 18) = 36\)
Calculatrice PPCM et PGCD
Calculer le plus petit commun multiple (PPCM) et le plus grand commun diviseur (PGCD) de deux nombres ou plus avec solutions détaillées étape par étape
Résultats
Entrez les valeurs et cliquez sur Calculer pour voir le résultat.
GCD and LCM
The Greatest Common Divisor (GCD) and Least Common Multiple (LCM) are fundamental concepts in number theory with practical applications in fractions, ratios, and problem-solving.
GCD (Greatest Common Divisor):
- The largest positive integer that divides each of the numbers
- Also called HCF (Highest Common Factor)
- Used for simplifying fractions
- Euclidean algorithm: GCD(a,b) = GCD(b, a mod b)
LCM (Least Common Multiple):
- The smallest positive integer divisible by all numbers
- Used for adding/subtracting fractions with different denominators
- Formula: LCM(a,b) = (a × b) / GCD(a,b)
- Can be found using prime factorization
Relationship:
- GCD(a,b) × LCM(a,b) = a × b (for two numbers)
- GCD divides both numbers, both numbers divide LCM
- If GCD(a,b) = 1, the numbers are coprime
Worked Examples
Example 2
\(\text{GCD}(24, 36, 48) = 12, \text{LCM}(24, 36, 48) = 144\)