The GCF of 12 and 40 is 4. The LCM of 12 and 40 is 120.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Common factors: 1, 2 and 4. The greatest of these is 4.
12 = 2 × 2 × 3
40 = 2 × 2 × 2 × 5
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 × 3 × 5 = 120.
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, 40) = 4.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ...
Multiples of 40: 40, 80, 120, 160, ...
The first number in both lists is 120.
4 × 120 = 480 = 12 × 40. This always holds for two numbers, so you can find the LCM as (12 × 40) ÷ 4 = 120.
Divide the top and bottom by the GCF 4: 12/40 = 3/10.
| 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 40 | 2 | 40 |
| 3 and 40 | 1 | 120 |
| 4 and 40 | 4 | 40 |
| 5 and 40 | 5 | 40 |
| 6 and 40 | 2 | 120 |
| 7 and 40 | 1 | 280 |
See also: factors of 12 · factors of 40.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.