LCM Calculator
Calculate the Least Common Multiple (LCM) of two or more numbers. Uses prime factorization to find the smallest number that is a multiple of all inputs.
Inputs
Results
Least Common Multiple (LCM)
36
Greatest Common Divisor (GCD)6
Numbers Calculated2
LCM Prime Factorization2^2 × 3^2
Calculation StepsStep 1: Find prime factorization of each number
• 12 = 2^2 × 3
• 18 = 2 × 3^2
Step 2: Take highest power of each prime factor
LCM = 2^2 × 3^2 = 36
How to Use This Calculator
- Enter two required integers and up to two optional additional integers in the Number fields.
- The Least Common Multiple is the smallest positive integer divisible by all entered numbers, computed as LCM(a,b) = |a × b| / GCD(a,b).
- LCM is essential when adding or subtracting fractions with unlike denominators — the LCM becomes the common denominator.
- For more than two numbers the calculator applies LCM iteratively: LCM(a,b,c) = LCM(LCM(a,b),c).
- Leave optional number fields at 0 to exclude them from the calculation.
- All inputs must be positive integers; the LCM of any number and 0 is undefined.
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Formula
LCM(a, b) = |a × b| / GCD(a, b)Related Calculators
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