The GCF of 30 and 40 is 10. The LCM of 30 and 40 is 120.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Common factors: 1, 2, 5 and 10. The greatest of these is 10.
30 = 2 × 3 × 5
40 = 2 × 2 × 2 × 5
GCF: multiply the prime factors both numbers share: 2 × 5 = 10.
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 10, so GCF(30, 40) = 10.
Multiples of 30: 30, 60, 90, 120, 150, ...
Multiples of 40: 40, 80, 120, 160, ...
The first number in both lists is 120.
10 × 120 = 1,200 = 30 × 40. This always holds for two numbers, so you can find the LCM as (30 × 40) ÷ 10 = 120.
Divide the top and bottom by the GCF 10: 30/40 = 3/4.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 30 | 2 | 30 |
| 3 and 30 | 3 | 30 |
| 4 and 30 | 2 | 60 |
| 5 and 30 | 5 | 30 |
| 6 and 30 | 6 | 30 |
| 7 and 30 | 1 | 210 |
| 2 and 40 | 2 | 40 |
| 3 and 40 | 1 | 120 |
| 4 and 40 | 4 | 40 |
| 5 and 40 | 5 | 40 |
| 6 and 40 | 2 | 120 |
| 7 and 40 | 1 | 280 |
See also: factors of 30 · factors of 40.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.