The GCF of 30 and 50 is 10. The LCM of 30 and 50 is 150.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1, 2, 5 and 10. The greatest of these is 10.
30 = 2 × 3 × 5
50 = 2 × 5 × 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 × 5 = 150.
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(30, 50) = 10.
Multiples of 30: 30, 60, 90, 120, 150, 180, ...
Multiples of 50: 50, 100, 150, 200, ...
The first number in both lists is 150.
10 × 150 = 1,500 = 30 × 50. This always holds for two numbers, so you can find the LCM as (30 × 50) ÷ 10 = 150.
Divide the top and bottom by the GCF 10: 30/50 = 3/5.
| Numbers | GCF | LCM |
|---|---|---|
| 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 |
| 2 and 50 | 2 | 50 |
| 3 and 50 | 1 | 150 |
| 4 and 50 | 2 | 100 |
| 5 and 50 | 5 | 50 |
| 6 and 50 | 2 | 150 |
| 7 and 50 | 1 | 350 |
See also: factors of 30 · factors of 50.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.