The GCF of 10 and 25 is 5. The LCM of 10 and 25 is 50.
Factors of 10: 1, 2, 5, 10.
Factors of 25: 1, 5, 25.
Common factors: 1 and 5. The greatest of these is 5.
10 = 2 × 5
25 = 5 × 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 × 5 × 5 = 50.
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(10, 25) = 5.
Multiples of 10: 10, 20, 30, 40, 50, 60, ...
Multiples of 25: 25, 50, 75, ...
The first number in both lists is 50.
5 × 50 = 250 = 10 × 25. This always holds for two numbers, so you can find the LCM as (10 × 25) ÷ 5 = 50.
Divide the top and bottom by the GCF 5: 10/25 = 2/5.
| 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 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 |
See also: factors of 10 · factors of 25.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.