GCD and LCM Calculator

How to use

1. 1Enter at least two positive whole numbers into the input fields. Click Add number to compare more than two; the calculator handles up to twelve at once. Underscores, spaces, and commas inside numbers are ignored, so 1_000_000 and 1,000,000 both work.
2. 2Read the GCD and LCM cards at the top. The GCD card highlights when the inputs are coprime (GCD equals 1) and the LCM card always shows the smallest positive number every input divides into.
3. 3Open the Euclidean algorithm panel to see the gcd(a, b) trace as a sequence of long-division lines, then copy the steps if you need to paste them into homework or a write-up.
4. 4Scroll to Prime factorization method to see each number broken into prime powers, the min/max exponent table, and the GCD and LCM written out as prime products.
5. 5Use the divisors of the GCD and the first multiples of the LCM panels to answer related questions: every common divisor is in the first list and every common multiple is a multiple of the LCM. Click Copy full result to grab everything as plain text.

About this tool

GCD and LCM Calculator finds the greatest common divisor and the least common multiple of any two or more positive integers, and shows the working in three ways at once. It runs the Euclidean algorithm and prints every long-division step (a = b * q + r) so you can copy the trace into a homework write-up or a code review. It builds the prime factorization of each input and lines up the shared primes in a table, with the minimum exponent column reading off as the GCD and the maximum exponent column reading off as the LCM, which is the textbook method most teachers expect to see. It also lists every divisor of the GCD and the first several multiples of the LCM, and for two-number inputs it verifies the identity gcd(a, b) times lcm(a, b) equals a times b. All math runs locally with JavaScript BigInt, so numbers of up to eighteen digits keep full precision and nothing you type is uploaded. The same machinery powers fraction simplification (divide the numerator and denominator by their GCD), common-denominator addition (use the LCM of the denominators), gear ratio and pulley sync problems, scheduling problems (when do two repeating events line up again?), tile and brick layout, and number-theory practice. Try the presets to see edge cases: coprime triples like 8, 9, 25 where the GCD collapses to 1; sets where one number divides the rest so the GCD equals the smallest input; and the classic fraction-denominator pair (6 and 8) that produces the smallest common denominator (24).

Free to use. Works in your browser. No signup, no login.