LCM Calculator — Least Common Multiple
Find the Least Common Multiple (LCM) of two or more numbers. See step-by-step calculation using prime factorization and the GCD method.
🔢 LCM Calculator
Result
Steps (using GCD method)
💡 What is the Least Common Multiple (LCM)?
The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by all of them. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.
There are three common methods to find the LCM: (1) Listing multiples of each number until you find the first common one — simple but slow for large numbers. (2) Prime factorization — decompose each number into primes, then take the highest power of each prime. (3) Using the GCD formula: LCM(a,b) = |a×b| / GCD(a,b) — the most efficient method, and the one our calculator uses.
The LCM is essential for adding and subtracting fractions (finding the least common denominator), scheduling problems (when will two events coincide?), and modular arithmetic. In real life, the LCM appears in gear systems, traffic light timing, and any situation where two periodic events need to synchronize.
Where:
- a, b = The two numbers
- GCD(a,b) = Greatest Common Divisor of a and b
- |a × b| = Absolute value of the product
📝 Worked Example
LCM(12, 18)
|12 × 18| / GCD(12, 18) = 216 / 6= 36
Alt: prime factorization
12=2²×3, 18=2×3² → 2²×3²= = 36