GCF and LCM Calculator
Number 1
Number 2
Results
How to Use
- Enter two or more numbers (positive integers)
- Add more numbers if needed using the "Add Another Number" button
- Click "Calculate GCF & LCM" to find both results
- The calculator will show both GCF and LCM with detailed steps
What are GCF and LCM?
Greatest Common Factor (GCF)
The largest positive integer that divides each of the numbers without leaving a remainder.
Example: GCF of 12 and 18
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
GCF = 6
Least Common Multiple (LCM)
The smallest positive integer that is divisible by each of the numbers.
Example: LCM of 12 and 18
Multiples of 12: 12, 24, 36, 48, ...
Multiples of 18: 18, 36, 54, 72, ...
LCM = 36
Relationship Between GCF and LCM
For any two numbers a and b:
GCF(a,b) × LCM(a,b) = a × b
Example: For 12 and 18
GCF(12,18) × LCM(12,18) = 6 × 36 = 216 = 12 × 18
Applications
GCF Applications:
- Simplifying fractions
- Finding equivalent fractions
- Solving word problems
- Algebraic expressions
LCM Applications:
- Adding/subtracting fractions
- Scheduling problems
- Finding common denominators
- Repeating patterns
Common Examples
| Numbers | GCF | LCM | Explanation |
|---|---|---|---|
| 8, 12 | 4 | 24 | 4 × 24 = 8 × 12 = 96 |
| 15, 20, 25 | 5 | 300 | Smallest number divisible by all three |
| 7, 13 | 1 | 91 | Prime numbers have GCF of 1 |
| 24, 36, 48 | 12 | 144 | Largest common factor and smallest common multiple |
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