The GCF of 10 and 30 is 10. The LCM of 10 and 30 is 30.
Factors of 10: 1, 2, 5, 10.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Common factors: 1, 2, 5 and 10. The greatest of these is 10.
10 = 2 × 5
30 = 2 × 3 × 5
GCF: multiply the prime factors both numbers share: 2 × 5 = 10.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 3 × 5 = 30.
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 10, so GCF(10, 30) = 10.
Multiples of 10: 10, 20, 30, 40, ...
Multiples of 30: 30, 60, ...
The first number in both lists is 30.
10 × 30 = 300 = 10 × 30. This always holds for two numbers, so you can find the LCM as (10 × 30) ÷ 10 = 30.
Divide the top and bottom by the GCF 10: 10/30 = 1/3.
| 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 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 10 · factors of 30.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.