Example 1
\(\text{GCD}(12, 18) = 6, \text{LCM}(12, 18) = 36\)
最小公倍数・最大公約数計算機
詳細なステップバイステップの解法で2つ以上の数の最小公倍数（LCM）と最大公約数（GCD）を計算
結果
値を入力して計算をクリックして結果を表示してください。
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
\(\text{GCD}(24, 36, 48) = 12, \text{LCM}(24, 36, 48) = 144\)