CalcCommonsHow to use
Enter integers separated by commas or spaces, then calculate. Read the exact LCM first and expand the steps to see each pairwise calculation. Use the GCF result to check the relationship between the two quantities.
For related tasks, try the Factoring Calculator.
Formula & how it works
LCM(a, b) = |a ÷ GCF(a, b) × b|. Apply this relation successively to more integers.
Worked examples
Example 1
For 12 and 18, GCF = 6. LCM = (12 ÷ 6) × 18 = 36.
Example 2
For 4, 6 and 10: LCM(4,6)=12, then LCM(12,10)=60.
Assumptions & practical notes
Calculations use exact integer arithmetic. Each input must be an integer of absolute value at most one billion.
A zero input makes the LCM zero by convention. Negative inputs are treated as positive magnitudes.
See our calculation methodology for unit definitions and testing practices.
References & measurement guidance
References explain the underlying mathematics. The examples and interactive calculations on this page are specific to CalcCommons.
Frequently asked questions
How is LCM different from GCF?
LCM is the smallest positive shared multiple for nonzero inputs. GCF is the largest positive shared divisor. For 12 and 18, they are 36 and 6 respectively.
Can I use this to add fractions?
Yes. The LCM of the denominators is the least common denominator. Rewrite the fractions with that denominator before adding.
Why does a zero input return zero?
We use the conventional extension LCM(a,0)=0. For positive nonzero inputs the usual smallest-positive-multiple definition applies.
Related calculators
Factoring Calculator
Find integer factors, greatest common factors, and rational factors of quadratic trinomials.
Fraction Calculator
Add, subtract, multiply, divide, and convert fractions, mixed numbers, and decimals.
Average Calculator
Find the arithmetic mean, sum, count, minimum, and maximum of a number list.