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Free least common multiple calculator for two to ten integers. Get the LCM, optional GCD for pairs, and prime factor breakdown—perfect for denominators, multiples, and discrete arithmetic practice.
Last updated: April 13, 2026
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LCM
60
LCM(12, 15) = 60
Prime factorizations
Tips
Idea
LCM(a,b,c) = LCM(LCM(a,b),c)
Add fields up to ten numbers for batch problems.
Rule
LCD = LCM of denominators
Pair with our simplify and fraction tools when needed.
Display
2² × 3 × 5 …
Matches how many textbooks teach hand calculation.
a × b = LCM(a,b) × GCD(a,b)
GCD appears when exactly two inputs are filled.
Middle school through intro number theory
Use for checks after manual ladder or factor trees.
Cycles of length m and n meet every LCM(m,n) steps
Explains real-world LCM word problems.
LCM(12, 15)
12 = 2^2 × 3, 15 = 3 × 5
LCM = 2^2 × 3 × 5 = 60
Inputs are parsed as positive integers. The tool applies the Euclidean algorithm for GCD of two numbers at a time, converts that to LCM via LCM(a,b) = |ab|/GCD(a,b), and folds across your list. Prime factors are found by trial division—fine for school-sized integers and the same approach many students use by hand on smaller numbers.
For each prime p, use the largest exponent appearing in any single factorization.Share it with students working on fractions or multiples
Suggested hashtags: #LCM #Math #Arithmetic #Education #Calculator