The GCF of 7 and 21 is 7. The LCM of 7 and 21 is 21.
Factors of 7: 1, 7.
Factors of 21: 1, 3, 7, 21.
Common factors: 1 and 7. The greatest of these is 7.
7 = 7 (prime)
21 = 3 × 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: 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 7, so GCF(7, 21) = 7.
Multiples of 7: 7, 14, 21, 28, ...
Multiples of 21: 21, 42, ...
The first number in both lists is 21.
7 × 21 = 147 = 7 × 21. This always holds for two numbers, so you can find the LCM as (7 × 21) ÷ 7 = 21.
Divide the top and bottom by the GCF 7: 7/21 = 1/3.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 7 | 1 | 14 |
| 3 and 7 | 1 | 21 |
| 4 and 7 | 1 | 28 |
| 5 and 7 | 1 | 35 |
| 6 and 7 | 1 | 42 |
| 7 and 8 | 1 | 56 |
| 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 |
| 8 and 21 | 1 | 168 |
See also: factors of 7 · factors of 21.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.