GCF and LCM Calculator – Greatest Common Factor and Least Common Multiple
Calculate the GCF (greatest common factor) and LCM (least common multiple) of any two or three numbers. Shows prime factorization method.
📊 Math📐 GCF = product of common prime factors | LCM = GCF × (a/GCF) × (b/GCF)
Number 1
Number 2
Number 3 (optional)
Please enter valid values.
Formula & Reference
| Variable | Formula | Units |
|---|---|---|
| GCF and LCM Calculator – Greatest Common Factor and Least Common Multiple | GCF = product of common prime factors | LCM = GCF × (a/GCF) × (b/GCF) | GCF / LCM |
Step-by-Step Examples
Example 1
GCF & LCM of 12 and 18
GCF = 6, LCM = 36.
- 12 = 2²×3 | 18 = 2×3²
- GCF = 2×3 = 6 | LCM = 2²×3² = 36
✓ GCF=6 / LCM=36
Example 2
Three Numbers: 4, 6, 10
GCF = 2, LCM = 60.
- GCF(4,6,10) = 2 | LCM(4,6,10) = 60
✓ GCF=2 / LCM=60
Example 3
Coprime Numbers: 7 and 13
GCF = 1 (coprime), LCM = 91.
- No common factors → GCF = 1 | LCM = 7×13 = 91
✓ GCF=1 / LCM=91
Real-World Applications
Math Students
Find GCF and LCM for fractions and word problems.
Teachers
Demonstrate factor concepts clearly.
Programmers
GCF for algorithms, LCM for scheduling.
Planners
LCM for repeating cycle problems.
Common Mistakes to Avoid
⚠️
GCF vs LCM — mixing them up
GCF: largest number that divides both evenly. LCM: smallest number divisible by both. For fractions: use GCF to simplify, LCM to find common denominator.
⚠️
GCF of 1
If GCF = 1, the numbers are coprime (no common factors). Their LCM = their product.
Frequently Asked Questions
What is the GCF? ▾
Greatest Common Factor — the largest number that divides evenly into all given numbers. GCF(12, 18) = 6 because 6 is the largest number dividing both.
What is the LCM? ▾
Least Common Multiple — the smallest number that all given numbers divide into evenly. LCM(4, 6) = 12 because 12 is the smallest multiple of both 4 and 6.
When do you use LCM? ▾
Adding/subtracting fractions (need common denominator). Scheduling problems (when two events next coincide). Converting units.
Related Calculators
Formula Explorer connections
Interpretation: This formula uses integer divisibility, modular arithmetic, finite fields or coding relationships. Assumption: Inputs are usually integers with specific modulus or coprimality requirements. Cryptographic examples are educational and not a substitute for vetted security libraries.