GCD & LCM Calculator

The calculator works on a list of integers - two input fields by default, with an Add button to append more and a trash icon to remove any once you have more than two. Each field is sanitized as you type so only digits and a single leading minus survive, and the result engine runs parseInt over the list and silently drops any entry that is NaN or zero, so you need at least two valid non-zero integers before anything is computed. The GCD is found with the classic Euclidean algorithm (a repeated `a mod b` loop until the remainder is zero), and because every value is passed through Math.abs first, negative inputs like -12 are treated by magnitude. For three or more numbers, both the GCD and LCM are reduced pairwise with a left fold - gcd(a, b, c) is computed as gcd(gcd(a, b), c) - rather than by any single multi-argument formula.

The LCM is derived from the identity lcm(a, b) = |a x b| / gcd(a, b) rather than by listing multiples, which keeps it exact for the pairwise fold. Because that product can grow quickly, the LCM panel switches to JavaScript exponential notation with four decimals (toExponential(4)) whenever the value exceeds 999,999,999,999, while smaller results use grouped thousands separators. Alongside the two headline numbers, the tool prints a prime factorization for each input using trial division up to the square root, formatted with caret exponents - so 12 renders as 2^2 x 3 and 18 as 2 x 3^2 - and a chip list of every common divisor, which it computes as the divisors of the GCD (the divisors of the GCD are exactly the divisors shared by all inputs).

When you enter exactly two numbers, an extra Verification panel demonstrates the GCD x LCM = |a x b| relationship explicitly: it shows GCD x LCM, evaluates that product, shows |a| x |b| beside it, and prints a green check mark when the two match. This panel only appears in the two-number case - it is not shown for three or more inputs, since the simple product identity does not generalize. Note that despite what older descriptions may suggest, the tool does not print an iterative step-by-step Euclidean trace; it shows the final GCD and LCM plus the factorization, common-divisor, and (for two numbers) verification panels. Every result recomputes instantly via a memoized hook as you edit fields, and both the GCD and LCM values have one-click copy buttons.