The GCF of 12 and 16 is 4. The LCM of 12 and 16 is 48.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 16: 1, 2, 4, 8, 16.
Common factors: 1, 2 and 4. The greatest of these is 4.
12 = 2 × 2 × 3
16 = 2 × 2 × 2 × 2
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 × 2 × 2 × 3 = 48.
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, 16) = 4.
Multiples of 12: 12, 24, 36, 48, 60, ...
Multiples of 16: 16, 32, 48, 64, ...
The first number in both lists is 48.
4 × 48 = 192 = 12 × 16. This always holds for two numbers, so you can find the LCM as (12 × 16) ÷ 4 = 48.
Divide the top and bottom by the GCF 4: 12/16 = 3/4.
| 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 16 | 2 | 16 |
| 3 and 16 | 1 | 48 |
| 4 and 16 | 4 | 16 |
| 5 and 16 | 1 | 80 |
| 6 and 16 | 2 | 48 |
| 7 and 16 | 1 | 112 |
See also: factors of 12 · factors of 16 · 12/16 as a decimal.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.