The GCF of 25 and 100 is 25. The LCM of 25 and 100 is 100.
Factors of 25: 1, 5, 25.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1, 5 and 25. The greatest of these is 25.
25 = 5 × 5
100 = 2 × 2 × 5 × 5
GCF: multiply the prime factors both numbers share: 5 × 5 = 25.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 5 × 5 = 100.
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 25, so GCF(25, 100) = 25.
Multiples of 25: 25, 50, 75, 100, 125, ...
Multiples of 100: 100, 200, ...
The first number in both lists is 100.
25 × 100 = 2,500 = 25 × 100. This always holds for two numbers, so you can find the LCM as (25 × 100) ÷ 25 = 100.
Divide the top and bottom by the GCF 25: 25/100 = 1/4.
| 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 100 | 2 | 100 |
| 3 and 100 | 1 | 300 |
| 4 and 100 | 4 | 100 |
| 5 and 100 | 5 | 100 |
| 6 and 100 | 2 | 300 |
| 7 and 100 | 1 | 700 |
See also: factors of 25 · factors of 100.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.