Calculate the greatest common divisor and least common multiple of two or more numbers with steps.
A single set of two or more positive integers yields both divisibility results: the greatest common divisor shared by every entry and the least common multiple divisible by every entry. The accompanying steps help verify how the inputs lead to each value. With three or more numbers, both answers concern the complete set, not separate pairs. This distinction matters because the overall GCD can be 1 even though some pairs in the set have larger common divisors.
A concrete input and expected output from the current implementation.
Input
18, 24, 30
Expected output
GCD = 6 LCM = 360
The prime factorizations are 18 = 2 * 3^2, 24 = 2^3 * 3, and 30 = 2 * 3 * 5. Shared factors at their lowest powers give 2 * 3 = 6, while all factors at their highest powers give 2^3 * 3^2 * 5 = 360.
For the GCD, the relevant factors are those shared by every entered integer. In a prime-factor view, keep only primes occurring in all entries and use the smallest exponent seen. For 18, 24, and 30, that leaves 2 * 3. The result is the greatest positive integer that divides the entire list without a remainder.
For the LCM, include every prime occurring in any entry and use the largest exponent required by any one entry. This gives the smallest positive integer divisible by each input. For two nonzero integers, LCM(a,b) * GCD(a,b) = |a * b| provides an independent check on the two reported values.
No. A whole-set GCD of 1 says only that no integer greater than 1 divides every entry. For example, GCD(6, 10, 15) is 1, but the three pairwise GCDs are 2, 3, and 5. If pairwise coprimality matters, calculate or inspect each pair separately.
Not generally. The product is a common multiple for positive integers, but it may repeat prime factors that are needed only once. For 12 and 18, the product is 216 while the LCM is 36. The product equals the LCM when the positive inputs are pairwise coprime; otherwise, use the calculated LCM.
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