The GCF of 12 and 18 is 6. The LCM of 12 and 18 is 36.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 18: 1, 2, 3, 6, 9, 18.
Common factors: 1, 2, 3 and 6. The greatest of these is 6.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
GCF: multiply the prime factors both numbers share: 2 × 3 = 6.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 3 = 36.
Divide the larger number by the smaller and repeat with the remainder until it is 0. The last non-zero remainder is the GCF.
The last non-zero remainder is 6, so GCF(12, 18) = 6.
Multiples of 12: 12, 24, 36, 48, ...
Multiples of 18: 18, 36, 54, ...
The first number in both lists is 36.
6 × 36 = 216 = 12 × 18. This always holds for two numbers, so you can find the LCM as (12 × 18) ÷ 6 = 36.
Divide the top and bottom by the GCF 6: 12/18 = 2/3.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 12 | 2 | 12 |
| 3 and 12 | 3 | 12 |
| 4 and 12 | 4 | 12 |
| 5 and 12 | 1 | 60 |
| 6 and 12 | 6 | 12 |
| 7 and 12 | 1 | 84 |
| 2 and 18 | 2 | 18 |
| 3 and 18 | 3 | 18 |
| 4 and 18 | 2 | 36 |
| 5 and 18 | 1 | 90 |
| 6 and 18 | 6 | 18 |
| 7 and 18 | 1 | 126 |
See also: factors of 12 · factors of 18 · 12/18 as a decimal.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.