LCM Calculator

LCM (Least Common Multiple) is the smallest positive integer divisible by all given numbers. Calculate using: LCM(a,b) = (a * b) / GCD(a,b). For multiple numbers, find LCM of first two, then LCM of result with third number. Example: LCM(12,18) = (12*18)/GCD(12,18) = 216/6 = 36. Common uses: finding common denominators in fractions, scheduling recurring events.

LCM (Least Common Multiple) is the smallest number divisible by all inputs - always >= largest input. GCD (Greatest Common Divisor) is the largest number that divides all inputs - always <= smallest input. Example: For 12 and 18, LCM = 36 (smallest multiple of both), GCD = 6 (largest divisor of both). LCM used for adding fractions, GCD for simplifying fractions.

Prime factorization method: 1) Find prime factors of each number. 2) Take highest power of each prime. 3) Multiply together. Example: LCM(12,18): 12 = 2^2*3, 18 = 2*3^2. Take 2^2 and 3^2 → LCM = 4*9 = 36. This method works well for multiple numbers and shows why LCM works. Alternative: list multiples until you find common one.

Real-world LCM applications: 1) Adding fractions with different denominators (find LCM for common denominator). 2) Scheduling: If event A occurs every 6 days and B every 8 days, they coincide every LCM(6,8)=24 days. 3) Gear ratios in mechanics. 4) Music theory (rhythm patterns). 5) Tiling/patterns (when rectangular tiles repeat). 6) Project management (task synchronization).

No, LCM is always >= the largest input number. It must be a multiple of all inputs, so it cannot be smaller than any of them. The smallest possible LCM equals the largest input number (when larger number is divisible by all others). Example: LCM(3,6,12) = 12 because 12 is already divisible by 3 and 6. If numbers are coprime (GCD=1), LCM equals their product: LCM(5,7)=35.