GCF and LCM Table
The greatest common factor (GCF), also called the greatest common divisor, is the largest number that divides two integers evenly. The least common multiple (LCM) is the smallest positive number that is a multiple of both. This page provides 1–12 reference grids for both, plus a calculator for any two numbers.
GCF and LCM Calculator
Enter two positive whole numbers to find their greatest common factor and least common multiple.
GCF(12, 18)6
LCM(12, 18)36
GCF (1–12) Grid
| GCF | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 |
| 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 |
| 4 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 4 |
| 5 | 1 | 1 | 1 | 1 | 5 | 1 | 1 | 1 | 1 | 5 | 1 | 1 |
| 6 | 1 | 2 | 3 | 2 | 1 | 6 | 1 | 2 | 3 | 2 | 1 | 6 |
| 7 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | 1 | 1 | 1 | 1 | 1 |
| 8 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 8 | 1 | 2 | 1 | 4 |
| 9 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 9 | 1 | 1 | 3 |
| 10 | 1 | 2 | 1 | 2 | 5 | 2 | 1 | 2 | 1 | 10 | 1 | 2 |
| 11 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 11 | 1 |
| 12 | 1 | 2 | 3 | 4 | 1 | 6 | 1 | 4 | 3 | 2 | 1 | 12 |
LCM (1–12) Grid
| LCM | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 2 | 6 | 4 | 10 | 6 | 14 | 8 | 18 | 10 | 22 | 12 |
| 3 | 3 | 6 | 3 | 12 | 15 | 6 | 21 | 24 | 9 | 30 | 33 | 12 |
| 4 | 4 | 4 | 12 | 4 | 20 | 12 | 28 | 8 | 36 | 20 | 44 | 12 |
| 5 | 5 | 10 | 15 | 20 | 5 | 30 | 35 | 40 | 45 | 10 | 55 | 60 |
| 6 | 6 | 6 | 6 | 12 | 30 | 6 | 42 | 24 | 18 | 30 | 66 | 12 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 7 | 56 | 63 | 70 | 77 | 84 |
| 8 | 8 | 8 | 24 | 8 | 40 | 24 | 56 | 8 | 72 | 40 | 88 | 24 |
| 9 | 9 | 18 | 9 | 36 | 45 | 18 | 63 | 72 | 9 | 90 | 99 | 36 |
| 10 | 10 | 10 | 30 | 20 | 10 | 30 | 70 | 40 | 90 | 10 | 110 | 60 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 11 | 132 |
| 12 | 12 | 12 | 12 | 12 | 60 | 12 | 84 | 24 | 36 | 60 | 132 | 12 |
How to Find GCF and LCM
- Prime factorization: write each number as a product of primes. The GCF is the product of the shared prime factors at their lowest power; the LCM is the product of all prime factors at their highest power. For 12 = 2² × 3 and 18 = 2 × 3², GCF = 2 × 3 = 6 and LCM = 2² × 3² = 36.
- Euclidean algorithm (GCF): repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is 0. The last non-zero remainder is the GCF.
- Formula: GCF(a, b) × LCM(a, b) = a × b, so once you know one you can find the other: LCM(a, b) = (a × b) / GCF(a, b).
Common Uses
- Simplifying fractions: divide numerator and denominator by their GCF. See the Fractions to Decimals Table.
- Adding and subtracting fractions: the LCM of the denominators gives the least common denominator.
- Scheduling and cycles: the LCM finds when two repeating events (e.g., buses arriving every 4 and 6 minutes) next coincide.