The GCF of 21 and 60 is 3. The LCM of 21 and 60 is 420.
Factors of 21: 1, 3, 7, 21.
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.
21 = 3 × 7
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 × 5 × 7 = 420.
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(21, 60) = 3.
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, ...
The first number in both lists is 420.
3 × 420 = 1,260 = 21 × 60. This always holds for two numbers, so you can find the LCM as (21 × 60) ÷ 3 = 420.
Divide the top and bottom by the GCF 3: 21/60 = 7/20.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 21 | 1 | 42 |
| 3 and 21 | 3 | 21 |
| 4 and 21 | 1 | 84 |
| 5 and 21 | 1 | 105 |
| 6 and 21 | 3 | 42 |
| 7 and 21 | 7 | 21 |
| 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 21 · factors of 60.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.