The GCF of 9 and 60 is 3. The LCM of 9 and 60 is 180.
Factors of 9: 1, 3, 9.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1 and 3. The greatest of these is 3.
9 = 3 × 3
60 = 2 × 2 × 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 × 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 3, so GCF(9, 60) = 3.
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
Multiples of 60: 60, 120, 180, 240, ...
The first number in both lists is 180.
3 × 180 = 540 = 9 × 60. This always holds for two numbers, so you can find the LCM as (9 × 60) ÷ 3 = 180.
Divide the top and bottom by the GCF 3: 9/60 = 3/20.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 9 | 1 | 18 |
| 3 and 9 | 3 | 9 |
| 4 and 9 | 1 | 36 |
| 5 and 9 | 1 | 45 |
| 6 and 9 | 3 | 18 |
| 7 and 9 | 1 | 63 |
| 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 9 · factors of 60.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.