How to use the LCM Calculator
- Type two or more positive whole numbers, separated by commas or spaces.
- The LCM and GCF appear instantly.
- Read the prime factorization and steps to check your homework.
What is the least common multiple?
The LCM of a set of numbers is the smallest positive number that every one of them divides into evenly. For 4 and 6, the multiples of 4 are 4, 8, 12, 16… and of 6 are 6, 12, 18…, so the LCM is 12. You need the LCM to add or subtract fractions with different denominators — it is the least common denominator.
Three ways to find the LCM
- List multiples of each number until you find the first one they share. Fine for small numbers.
- Prime factorization: break each number into primes and multiply the highest power of every prime that appears. 12 = 2²·3, 18 = 2·3², 30 = 2·3·5 → LCM = 2²·3²·5 = 180.
- Using the GCF: for two numbers, LCM(a, b) = a × b ÷ GCF(a, b). For 12 and 18: 216 ÷ 6 = 36.
LCM vs GCF
The greatest common factor (also called the greatest common divisor, GCD, or highest common factor, HCF) is the largest number that divides all of them. It uses the lowest power of each shared prime: GCF(12, 18, 30) = 2·3 = 6. Use the GCF to simplify fractions, and the LCM to find common denominators.
Check whether your LCM answer is least
Enter your proposed answer to check divisibility and minimality. The checker identifies a non-zero remainder or explains when an answer is a common multiple but a smaller valid one exists.