GCD vs LCM is a choice about direction. Greatest common divisor looks downward: the largest integer that divides both numbers. Least common multiple looks upward: the smallest non-negative integer that both numbers divide (with a special case at zero). gcd(12, 18) is 6. lcm(12, 18) is 36. Those are not two names for one button.
The GCD & LCM Calculator returns both for two integers so you can see them together. It does not decide which one your word problem wanted. This article is that decision, plus the rules the tool actually implements for zero, negatives, and decimals.
Use GCD to reduce. 12/18 and 12 : 18 both divide by 6. The Fraction Calculator and the Ratio Calculator perform that reduction inside their own jobs. Open the GCD page when the question is only “what is the largest shared group”: tiling a 12 by 18 rectangle with the largest equal squares, splitting 12 and 18 items into the largest identical teams, or checking that two integers are coprime (gcd 1).
Coprime pairs are not a special mode. The Euclidean algorithm already returns 1. Their LCM is then the absolute product. If a worksheet asks you to “simplify,” it almost always wants GCD, not LCM.
Use LCM when two repeating events must land on the same step: a light that blinks every 12 seconds and another every 18 seconds meet every 36 seconds. Use it when two cycle lengths must share a future mark, or when you need a common denominator and you prefer the least one. Adding 1/12 + 1/18 uses denominator 36, which is lcm(12, 18). The Fraction Calculator finds that denominator as part of addition; you do not have to pre-compute LCM unless the question asked for it.
LCM is the wrong answer to “reduce.” Reporting 36 when the teacher wanted 6 is not a rounding error. It is the other function.
For nonzero a and b, gcd(a, b) × lcm(a, b) = |a × b|. 6 × 36 = 216 = 12 × 18. You can check a result with that identity. If the product of your gcd and lcm does not equal the absolute product of the inputs, one of the three numbers is wrong. The identity fails at zero, which is why 0 is documented instead of being forced through the same multiply.
gcd(0, n) is |n|. lcm(0, n) is 0 when n is not also 0. gcd(0, 0) is 0 on this page; lcm(0, 0) is undefined and labeled that way. Negatives are allowed; GCD uses absolute values and LCM is reported as a non-negative integer. −12 and 18 give 6 and 36, the same as 12 and 18.
A decimal such as 12.5 is an error, not a cast to 12. Truncation would change the question. Scientific notation is accepted only when it is still a whole number. 1e3 is 1000. 1e-1 is not an integer.
The form takes two integers. A list of twelve values would need an overflow check on every pairwise LCM and a worse layout. Run the tool again on (gcd so far, next) or (lcm so far, next). Products that leave JavaScript’s safe integer range are refused rather than rounded. That is stricter than a pocket calculator that would give you a float and call it an LCM.
For the fraction or ratio those integers came from, use the matching page after you understand gcd vs lcm. Reducing 12/18 is the Fraction Calculator. Reducing 12 : 18 is the Ratio Calculator. How they sit next to each other is in fractions, ratios, and proportions.
Ask whether you are looking for a shared factor or a shared future multiple. GCD is the factor. LCM is the multiple. Compute both when you want the check from the product identity. Report one when the sentence only asked for one. The other number sitting on the same result row is not a hint to average them.
GCD is the largest integer that divides both inputs. LCM is the smallest non-negative integer that both inputs divide, with 0 when either input is 0 and undefined for 0 and 0.
GCD. gcd(12, 18) = 6, so 12/18 = 2/3. LCM is not the reduction step.
The fields are integers. A decimal is an error so 12.7 is never silently truncated to 12.
Two fields keep zero and overflow visible. You can run the tool again on (gcd so far, next).
