GCF and LCM calculator: find the greatest common factor and least common multiple of two or more numbers instantly. Free, runs in your browser, no signup.
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GCF and LCM calculator: find the greatest common factor and least common multiple of two or more numbers instantly. Free, runs in your browser, no signup.
LCM of 12 and 18 is 36, not 216.
Transparent methodology
How this calculator works
Reviewed August 2026 · BoringToolsKit Editorial Team
Formula
GCF: largest integer dividing both numbers (Euclid). LCM = a x b / GCF.
BoringToolsKit. “GCF and LCM Calculator.” boringtoolskit.com/gcf-lcm-calculator/ (reviewed August 2026). Free to reference in articles, syllabi, and answer posts with a link.
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Worked example: GCF and LCM of 12 and 18
Enter 12 for a and 18 for b. The page runs the Euclidean algorithm on the pair: divide 18 by 12, remainder 6; divide 12 by 6, remainder 0. The last nonzero remainder is 6, so GCF = 6. No factoring was needed, which is exactly why the algorithm is preferred: it stays fast even when the inputs are large.
The LCM then falls out of the identity LCM = (a x b) / GCF. Here that is (12 x 18) / 6 = 216 / 6 = 36. You can confirm it by listing multiples: 12, 24, 36 and 18, 36, so 36 is the smallest shared one. Note that 36 is smaller than the raw product 216 by a factor of exactly the GCF, which is why dividing by GCF matters: skipping it gives the product, not the least common multiple.
The prime factorization view agrees: 12 = 2^2 x 3 and 18 = 2 x 3^2. Take the lowest power of each shared prime for GCF (2^1 x 3^1 = 6) and the highest power for LCM (2^2 x 3^2 = 36).
Edge cases the input check deliberately blocks
The page requires both values to be integers of at least 1, so a few inputs that have valid mathematics get rejected. GCF(0, 8) is conventionally 8, and GCF of negatives is well-defined via absolute values, but the calculator returns its Check inputs message instead. Treat 0 and negatives as out of scope rather than bugs.
Precision is the practical limit at the top end. JavaScript numbers are 64-bit floats, exact only up to 2^53, which is 9,007,199,254,740,992. Inputs near that ceiling can round silently before the algorithm runs. There is also an overflow risk in the LCM: for a = b = 3,037,000,497 (both prime), the product a x b is about 9.2 x 10^18, above the exact-integer range, so the displayed LCM may be off by a small amount even though GCF = 3,037,000,497 is correct. Keep both inputs under roughly 1 billion if you need the LCM to be trustworthy.
The calculator computes one pair at a time. For three or more numbers, chain it: GCF(24, 36, 60) is GCF(GCF(24, 36), 60) = GCF(12, 60) = 12, and the LCM chains the same way, LCM(LCM(24, 36), 60) = LCM(72, 60) = 360.
