The GCF of 18 and 60 is 6. The LCM of 18 and 60 is 180.
Factors of 18: 1, 2, 3, 6, 9, 18.
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.
18 = 2 × 3 × 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 × 3 × 5 = 180.
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(18, 60) = 6.
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, ...
Multiples of 60: 60, 120, 180, 240, ...
The first number in both lists is 180.
6 × 180 = 1,080 = 18 × 60. This always holds for two numbers, so you can find the LCM as (18 × 60) ÷ 6 = 180.
Divide the top and bottom by the GCF 6: 18/60 = 3/10.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 18 | 2 | 18 |
| 3 and 18 | 3 | 18 |
| 4 and 18 | 2 | 36 |
| 5 and 18 | 1 | 90 |
| 6 and 18 | 6 | 18 |
| 7 and 18 | 1 | 126 |
| 2 and 60 | 2 | 60 |
| 3 and 60 | 3 | 60 |
| 4 and 60 | 4 | 60 |
| 5 and 60 | 5 | 60 |
| 6 and 60 | 6 | 60 |
| 7 and 60 | 1 | 420 |
See also: factors of 18 · factors of 60.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.