GCD / LCM Calculator
Enter integers to calculate GCD (HCF) and LCM. Supports multiple numbers (comma-separated) and shows Euclidean steps for the first two.
Integers only. Examples: 12,18 · 24, 60, 90 · negatives allowed.
Privacy: calculations run locally in your browser. No inputs are stored or transmitted.
How it works
GCD (Euclidean algorithm): repeatedly apply division with remainder until remainder is 0.
LCM: for two numbers, LCM(a,b) = |a×b| ÷ GCD(a,b) (when not both 0).
For multiple numbers, compute pairwise: GCD(a,b,c) = GCD(GCD(a,b),c), similarly for LCM.
Examples
- 12, 18 → GCD = 6, LCM = 36
- 24, 60, 90 → GCD = 6, LCM = 360
- -8, 12 → GCD = 4, LCM = 24
- 10, 0 → GCD = 10, LCM = 0
FAQ
- What is GCD (greatest common divisor)?
GCD is the largest positive integer that divides each number with no remainder. It is also called HCF.
- What is LCM (least common multiple)?
LCM is the smallest positive integer that is a multiple of each number.
- Can I enter more than two numbers?
Yes. Enter a comma-separated list like 12, 18, 30. The calculator reduces pairwise across the list.
- Do negative numbers work?
Yes. GCD and LCM are computed using absolute values. LCM is reported as a positive number.
- What about zeros?
GCD(a, 0) = |a|. LCM(a, 0) is 0 by convention. If all inputs are 0, both results are 0.
- How are GCD and LCM related?
For two integers a and b (not both 0), |a×b| = GCD(a,b) × LCM(a,b).