Last updated: July 31, 2026
GCD Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
gcd via Euclidean algorithm; lcm = |a×b| / gcd
Where:
- a=First Integer
- b=Second Integer
Worked Examples
Standard pair
Find gcd and lcm for 84 and 30.
- 1Euclidean steps give gcd=6
- 2Compute lcm=|84×30|/6
- 3lcm=420
One value zero
Find gcd and lcm for 0 and 45.
- 1gcd(0,45)=45
- 2LCM with zero is 0
- 3Return both values
Negative integers
Find gcd and lcm for -27 and 36.
- 1Use absolute values in gcd steps
- 2gcd=9
- 3lcm=|(-27×36)|/9=108
Introduction
The GCD measures common divisibility, while LCM finds the smallest shared multiple for integer pair analysis.
Formula and Method
GCD Calculator applies gcd via Euclidean algorithm; lcm = |a×b| / gcd and returns deterministic outputs from validated inputs.
Validate each required input
Apply the stated formula
Round numeric outputs where needed
Return safe defaults when validation fails
Input Fields
Use these keys exactly as defined in calculation.ts.
- 1
a: First Integer
- 2
b: Second Integer
Output Fields
These values map directly to calculation.ts return keys.
- 1
gcd: Largest integer dividing both values
- 2
lcm: Smallest positive multiple shared by both values
Validation Rules
Inputs must be integers and not both zero.
Finite numeric values are required
Domain restrictions are enforced before solving
Invalid input returns default-safe outputs
Check examples to confirm expected behavior
How to Use This Calculator
Enter inputs, run the calculation, and read the primary output first.
Enter all required values
Click calculate
Review primary output first
Use supporting outputs for interpretation
Practical Uses
This calculator is useful for study, verification, and fast applied math checks.
Fraction simplification
Scheduling and cyclic events
Number theory learning
Algorithmic preprocessing
FAQs
What does the GCD Calculator compute?
It computes Greatest Common Divisor and supporting outputs from your inputs.
Which inputs are required?
Required inputs are: First Integer, Second Integer.
How are invalid inputs handled?
When validation fails, the calculator returns safe default values and does not attempt invalid math.
Are results rounded?
Yes. Numeric outputs are rounded inside calculation.ts (typically to 6 decimal places).
Can I use negative or decimal values?
Integer inputs are required; negative integers are supported via absolute-value logic.
How should I verify my answer?
Use the worked examples and compare each output key with your manual steps.