The GCF of 3 and 21 is 3. The LCM of 3 and 21 is 21.
Factors of 3: 1, 3.
Factors of 21: 1, 3, 7, 21.
Common factors: 1 and 3. The greatest of these is 3.
3 = 3 (prime)
21 = 3 × 7
GCF: multiply the prime factors both numbers share: 3 = 3.
LCM: multiply every prime the maximum number of times it appears in either number: 3 × 7 = 21.
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(3, 21) = 3.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
Multiples of 21: 21, 42, ...
The first number in both lists is 21.
3 × 21 = 63 = 3 × 21. This always holds for two numbers, so you can find the LCM as (3 × 21) ÷ 3 = 21.
Divide the top and bottom by the GCF 3: 3/21 = 1/7.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 3 | 1 | 6 |
| 3 and 4 | 1 | 12 |
| 3 and 5 | 1 | 15 |
| 3 and 6 | 3 | 6 |
| 3 and 7 | 1 | 21 |
| 3 and 8 | 1 | 24 |
| 2 and 21 | 1 | 42 |
| 4 and 21 | 1 | 84 |
| 5 and 21 | 1 | 105 |
| 6 and 21 | 3 | 42 |
| 7 and 21 | 7 | 21 |
| 8 and 21 | 1 | 168 |
See also: factors of 3 · factors of 21.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.