The GCF of 6 and 45 is 3. The LCM of 6 and 45 is 90.
Factors of 6: 1, 2, 3, 6.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1 and 3. The greatest of these is 3.
6 = 2 × 3
45 = 3 × 3 × 5
GCF: multiply the prime factors both numbers share: 3 = 3.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 3 × 3 × 5 = 90.
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 3, so GCF(6, 45) = 3.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ...
Multiples of 45: 45, 90, 135, ...
The first number in both lists is 90.
3 × 90 = 270 = 6 × 45. This always holds for two numbers, so you can find the LCM as (6 × 45) ÷ 3 = 90.
Divide the top and bottom by the GCF 3: 6/45 = 2/15.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 6 | 2 | 6 |
| 3 and 6 | 3 | 6 |
| 4 and 6 | 2 | 12 |
| 5 and 6 | 1 | 30 |
| 6 and 7 | 1 | 42 |
| 6 and 8 | 2 | 24 |
| 2 and 45 | 1 | 90 |
| 3 and 45 | 3 | 45 |
| 4 and 45 | 1 | 180 |
| 5 and 45 | 5 | 45 |
| 7 and 45 | 1 | 315 |
| 8 and 45 | 1 | 360 |
See also: factors of 6 · factors of 45.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.