GCD and LCM calculator for a list of integers

Worked result

GCD 6; LCM 360.

1. Use repeated remainders to find common divisors.
2. Accumulate the greatest common divisor across the list.
3. Accumulate least common multiples using division before multiplication.

Find the GCD and LCM of 18, 24 and 30

First combine 18 with 24, then combine that result with 30. The pairwise method extends to a longer list.

gcd(18, 24) = 6
gcd(6, 30) = 6
lcm(18, 24) = 18/6 × 24 = 72
gcd(72, 30) = 6
lcm(72, 30) = 72/6 × 30 = 360

The GCD divides every supplied integer. Every nonzero supplied integer divides the LCM. These two checks are useful for catching an accidental factor-versus-multiple swap.

Repeated remainders avoid trial factoring

Euclid’s algorithm replaces a pair (a, b) with (b, a mod b) until the second value is zero. The remaining nonnegative value is the greatest common divisor.

For two nonzero integers, their least common multiple is the absolute product divided by the greatest common divisor. Dividing first avoids an unnecessary large intermediate product. The tool combines pairs until it has processed the full list.

gcd(a, b) = gcd(b, a mod b)
lcm(a, b) = |a/gcd(a, b) × b| when both are nonzero
gcd(0, a) = |a|; gcd(0, 0) = 0
lcm(0, a) = 0

Input limits and common mistakes

Enter whole integers only, with at most 256 digits per integer and at most 50 entries. Decimal points and exponents are rejected even when they could represent a whole number.

The tool uses gcd(0, 0) = 0 and a zero least common multiple when any input is zero, following common computational conventions. This convention does not mean zero is a positive common multiple.

Questions about gcd and lcm

Sources and verification

These references explain the formulas or formats. The worked examples above were created for this tool and checked against independent calculations or format round trips. AI-assisted development does not imply a named human expert review.

• Python math reference: GCD and LCM — Integer definitions and zero conventions; examples checked independently in Python.

Published 2026-10-23. Examples are illustrations, not measurements of a service or claims about search rankings.

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Further reading

• Mathematics self-study roadmap and practice checkpoints