The GCF of 6 and 60 is 6. The LCM of 6 and 60 is 60.
Factors of 6: 1, 2, 3, 6.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1, 2, 3 and 6. The greatest of these is 6.
6 = 2 × 3
60 = 2 × 2 × 3 × 5
GCF: multiply the prime factors both numbers share: 2 × 3 = 6.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 5 = 60.
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 6, so GCF(6, 60) = 6.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ...
Multiples of 60: 60, 120, ...
The first number in both lists is 60.
6 × 60 = 360 = 6 × 60. This always holds for two numbers, so you can find the LCM as (6 × 60) ÷ 6 = 60.
Divide the top and bottom by the GCF 6: 6/60 = 1/10.
| 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 60 | 2 | 60 |
| 3 and 60 | 3 | 60 |
| 4 and 60 | 4 | 60 |
| 5 and 60 | 5 | 60 |
| 7 and 60 | 1 | 420 |
| 8 and 60 | 4 | 120 |
See also: factors of 6 · factors of 60.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.