The GCF of 10 and 12 is 2. The LCM of 10 and 12 is 60.
Factors of 10: 1, 2, 5, 10.
Factors of 12: 1, 2, 3, 4, 6, 12.
Common factors: 1 and 2. The greatest of these is 2.
10 = 2 × 5
12 = 2 × 2 × 3
GCF: multiply the prime factors both numbers share: 2 = 2.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 5 = 60.
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 2, so GCF(10, 12) = 2.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, ...
The first number in both lists is 60.
2 × 60 = 120 = 10 × 12. This always holds for two numbers, so you can find the LCM as (10 × 12) ÷ 2 = 60.
Divide the top and bottom by the GCF 2: 10/12 = 5/6.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 10 | 2 | 10 |
| 3 and 10 | 1 | 30 |
| 4 and 10 | 2 | 20 |
| 5 and 10 | 5 | 10 |
| 6 and 10 | 2 | 30 |
| 7 and 10 | 1 | 70 |
| 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 |
See also: factors of 10 · factors of 12 · 10/12 as a decimal.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.