The GCF of 21 and 28 is 7. The LCM of 21 and 28 is 84.
Factors of 21: 1, 3, 7, 21.
Factors of 28: 1, 2, 4, 7, 14, 28.
Common factors: 1 and 7. The greatest of these is 7.
21 = 3 × 7
28 = 2 × 2 × 7
GCF: multiply the prime factors both numbers share: 7 = 7.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 7 = 84.
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 7, so GCF(21, 28) = 7.
Multiples of 21: 21, 42, 63, 84, 105, ...
Multiples of 28: 28, 56, 84, 112, ...
The first number in both lists is 84.
7 × 84 = 588 = 21 × 28. This always holds for two numbers, so you can find the LCM as (21 × 28) ÷ 7 = 84.
Divide the top and bottom by the GCF 7: 21/28 = 3/4.
| 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 28 | 2 | 28 |
| 3 and 28 | 1 | 84 |
| 4 and 28 | 4 | 28 |
| 5 and 28 | 1 | 140 |
| 6 and 28 | 2 | 84 |
| 7 and 28 | 7 | 28 |
See also: factors of 21 · factors of 28.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.