The GCF of 25 and 30 is 5. The LCM of 25 and 30 is 150.
Factors of 25: 1, 5, 25.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Common factors: 1 and 5. The greatest of these is 5.
25 = 5 × 5
30 = 2 × 3 × 5
GCF: multiply the prime factors both numbers share: 5 = 5.
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 5, so GCF(25, 30) = 5.
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, ...
Multiples of 30: 30, 60, 90, 120, 150, 180, ...
The first number in both lists is 150.
5 × 150 = 750 = 25 × 30. This always holds for two numbers, so you can find the LCM as (25 × 30) ÷ 5 = 150.
Divide the top and bottom by the GCF 5: 25/30 = 5/6.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 25 | 1 | 50 |
| 3 and 25 | 1 | 75 |
| 4 and 25 | 1 | 100 |
| 5 and 25 | 5 | 25 |
| 6 and 25 | 1 | 150 |
| 7 and 25 | 1 | 175 |
| 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 25 · factors of 30.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.