Least Common Multiple Calculator
Calculate the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of multiple numbers with detailed prime factorization steps.
Calculate the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of multiple numbers with detailed prime factorization steps.
Enter Numbers
Enter positive integers separated by commas
About LCM and GCD
The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all the given numbers. The Greatest Common Divisor (GCD) is the largest positive integer that divides all the given numbers without a remainder.
Key Properties:
- • LCM(a, b) × GCD(a, b) = a × b
- • LCM is associative: LCM(a, LCM(b, c)) = LCM(LCM(a, b), c)
- • GCD is associative: GCD(a, GCD(b, c)) = GCD(GCD(a, b), c)
- • LCM of prime numbers is their product
- • GCD of coprime numbers is 1
Common Applications:
- • Finding common denominators for fractions
- • Scheduling and timing problems
- • Cryptography and number theory
- • Computer science algorithms
- • Mathematical problem solving
Calculation Method:
LCM is calculated using prime factorization. For each prime factor, we take the highest power that appears in any of the numbers. GCD is calculated using the Euclidean algorithm, which is efficient for large numbers.