The GCF of 15 and 100 is 5. The LCM of 15 and 100 is 300.
Factors of 15: 1, 3, 5, 15.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1 and 5. The greatest of these is 5.
15 = 3 × 5
100 = 2 × 2 × 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 × 2 × 3 × 5 × 5 = 300.
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(15, 100) = 5.
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, ...
Multiples of 100: 100, 200, 300, 400, ...
The first number in both lists is 300.
5 × 300 = 1,500 = 15 × 100. This always holds for two numbers, so you can find the LCM as (15 × 100) ÷ 5 = 300.
Divide the top and bottom by the GCF 5: 15/100 = 3/20.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 15 | 1 | 30 |
| 3 and 15 | 3 | 15 |
| 4 and 15 | 1 | 60 |
| 5 and 15 | 5 | 15 |
| 6 and 15 | 3 | 30 |
| 7 and 15 | 1 | 105 |
| 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 15 · factors of 100.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.