The GCF of 8 and 30 is 2. The LCM of 8 and 30 is 120.
Factors of 8: 1, 2, 4, 8.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Common factors: 1 and 2. The greatest of these is 2.
8 = 2 × 2 × 2
30 = 2 × 3 × 5
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 × 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 2, so GCF(8, 30) = 2.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
Multiples of 30: 30, 60, 90, 120, 150, ...
The first number in both lists is 120.
2 × 120 = 240 = 8 × 30. This always holds for two numbers, so you can find the LCM as (8 × 30) ÷ 2 = 120.
Divide the top and bottom by the GCF 2: 8/30 = 4/15.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 8 | 2 | 8 |
| 3 and 8 | 1 | 24 |
| 4 and 8 | 4 | 8 |
| 5 and 8 | 1 | 40 |
| 6 and 8 | 2 | 24 |
| 7 and 8 | 1 | 56 |
| 2 and 30 | 2 | 30 |
| 3 and 30 | 3 | 30 |
| 4 and 30 | 2 | 60 |
| 5 and 30 | 5 | 30 |
| 6 and 30 | 6 | 30 |
| 7 and 30 | 1 | 210 |
See also: factors of 8 · factors of 30.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.