The GCF of 12 and 28 is 4. The LCM of 12 and 28 is 84.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 28: 1, 2, 4, 7, 14, 28.
Common factors: 1, 2 and 4. The greatest of these is 4.
12 = 2 × 2 × 3
28 = 2 × 2 × 7
GCF: multiply the prime factors both numbers share: 2 × 2 = 4.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 7 = 84.
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 4, so GCF(12, 28) = 4.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, ...
Multiples of 28: 28, 56, 84, 112, ...
The first number in both lists is 84.
4 × 84 = 336 = 12 × 28. This always holds for two numbers, so you can find the LCM as (12 × 28) ÷ 4 = 84.
Divide the top and bottom by the GCF 4: 12/28 = 3/7.
| 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 28 | 2 | 28 |
| 3 and 28 | 1 | 84 |
| 4 and 28 | 4 | 28 |
| 5 and 28 | 1 | 140 |
| 6 and 28 | 2 | 84 |
| 7 and 28 | 7 | 28 |
See also: factors of 12 · factors of 28.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.