The GCF of 10 and 24 is 2. The LCM of 10 and 24 is 120.
Factors of 10: 1, 2, 5, 10.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Common factors: 1 and 2. The greatest of these is 2.
10 = 2 × 5
24 = 2 × 2 × 2 × 3
GCF: multiply the prime factors both numbers share: 2 = 2.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 3 × 5 = 120.
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 2, so GCF(10, 24) = 2.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
Multiples of 24: 24, 48, 72, 96, 120, 144, ...
The first number in both lists is 120.
2 × 120 = 240 = 10 × 24. This always holds for two numbers, so you can find the LCM as (10 × 24) ÷ 2 = 120.
Divide the top and bottom by the GCF 2: 10/24 = 5/12.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 10 | 2 | 10 |
| 3 and 10 | 1 | 30 |
| 4 and 10 | 2 | 20 |
| 5 and 10 | 5 | 10 |
| 6 and 10 | 2 | 30 |
| 7 and 10 | 1 | 70 |
| 2 and 24 | 2 | 24 |
| 3 and 24 | 3 | 24 |
| 4 and 24 | 4 | 24 |
| 5 and 24 | 1 | 120 |
| 6 and 24 | 6 | 24 |
| 7 and 24 | 1 | 168 |
See also: factors of 10 · factors of 24.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.