The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all given numbers.

How do I add fractions using LCM?

Find the LCM of the denominators. Use it as the common denominator and scale each fraction numerator accordingly.

What is the difference between LCM and GCF?

LCM is the smallest common multiple; GCF is the largest common factor. GCF(a,b) × LCM(a,b) = a × b.

LCM Calculator

Enter two or more positive integers to find their Least Common Multiple (LCM) — the smallest positive integer divisible by all of them — along with the GCF and first five common multiples.

How to use this calculator

Enter two or more positive integers, separated by commas or spaces.
Read the LCM and the first five common multiples as a reference.

Formula & method

LCM from GCF

LCM(a, b) = (a × b) / GCF(a, b) · For n numbers: LCM(LCM(a, b), c), …

GCF computed via Euclidean algorithm. Avoids overflow by computing GCF first before multiplying.

Example

LCM(12, 18, 30): LCM(12,18) = 36, LCM(36,30) = 180. First multiples: 180, 360, 540, 720, 900.

Key insights

LCM is the smallest number that all inputs divide into exactly.
LCM(a, b) = (a × b) / GCF(a, b) — using the GCF is the most efficient computation.
Adding fractions requires finding the LCM of the denominators as the common denominator: 1/4 + 1/6 → LCM(4, 6) = 12 → 3/12 + 2/12 = 5/12.
LCM is used in scheduling: if event A repeats every 4 days and B every 6 days, they coincide every LCM(4, 6) = 12 days.

How to interpret your result

LCM vs GCF

LCM is the smallest shared multiple; GCF is the largest shared factor. GCF × LCM = a × b for two numbers.

Common multiples

All common multiples of a set of numbers are multiples of their LCM: 12, 24, 36, 48, 60, … for LCM(4, 6) = 12.

Frequently asked questions

What is the LCM?: The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all given numbers.
How do I add fractions using LCM?: Find the LCM of the denominators. Use it as the common denominator and scale each fraction numerator accordingly.
What is the difference between LCM and GCF?: LCM is the smallest common multiple; GCF is the largest common factor. GCF(a,b) × LCM(a,b) = a × b.

Related calculators

GCF Calculator — Find the Greatest Common Factor (GCF/GCD) and all common factors of two or more integers using the Euclidean algorithm.
Fraction Calculator — Add, subtract, multiply, and divide fractions with step-by-step simplification and mixed number conversions.
Long Division Calculator — Perform integer long division with remainder, mixed number result, and step-by-step verification.

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