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GCD and LCM Calculator

Computes the greatest common divisor (highest common factor) and least common multiple of two or more integers with the Euclidean algorithm.

When to use

You need the GCD/HCF or LCM of a list of integers, e.g. to reduce fractions, find a common denominator or check whether numbers are coprime.

Do not use when: You need the prime factors themselves (use prime-factorization) or want to reduce a single fraction (use fraction-simplifier).

Formula

gcd(a, b) by the Euclidean algorithm (gcd(a, b) = gcd(b, a mod b)); lcm(a, b) = |a × b| / gcd(a, b); both are folded over the list: gcd(a, b, c) = gcd(gcd(a, b), c)

Inputs

Parameter	Type	Unit	Required	Description
`numbers`	number_list		yes	Two or more integers, comma-separated (e.g. 12, 18, 24). Negative values are treated by their absolute value.

Outputs

Output	Type	Description
`gcd`	integer	Greatest common divisor of all the numbers.
`lcm`	integer	Least common multiple of all the numbers.
`coprime`	boolean	true when the GCD is 1 (the numbers share no common factor).

Example

12 and 18: {"numbers":[12,18]} → {"gcd":6,"lcm":36,"coprime":false}

4, 6 and 8: {"numbers":[4,6,8]} → {"gcd":2,"lcm":24,"coprime":false}

GET https://tttkmbb.com/api/v1/calculate/gcd-lcm?numbers=12%2C18

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/gcd-lcm (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/gcd-lcm · Markdown: https://tttkmbb.com/math/gcd-lcm.md · JSON definition: https://tttkmbb.com/math/gcd-lcm.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="gcd-lcm"
OpenAPI operationId: calculate_gcd_lcm
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Greatest common divisor (reference)
Wikipedia – Least common multiple (reference)
Wolfram MathWorld – Greatest Common Divisor (reference)

FAQ

Is HCF the same as GCD?

Yes. Highest common factor (HCF), greatest common factor (GCF) and greatest common divisor (GCD) are the same quantity.

How large can the numbers be?

Any integers whose LCM stays below 2^53 (about 9 × 10^15); larger results cannot be represented exactly and return an error.

Related calculators

Fraction Simplifier — Reduce a fraction by its GCD.
Prime Factorization Calculator — See the prime factors behind the GCD and LCM.
Ratio Calculator — Simplify a ratio by dividing by the GCD.