The GCF of 30 and 36 is 6. The LCM of 30 and 36 is 180.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Common factors: 1, 2, 3 and 6. The greatest of these is 6.
30 = 2 × 3 × 5
36 = 2 × 2 × 3 × 3
GCF: multiply the prime factors both numbers share: 2 × 3 = 6.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 3 × 5 = 180.
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 6, so GCF(30, 36) = 6.
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, ...
Multiples of 36: 36, 72, 108, 144, 180, 216, ...
The first number in both lists is 180.
6 × 180 = 1,080 = 30 × 36. This always holds for two numbers, so you can find the LCM as (30 × 36) ÷ 6 = 180.
Divide the top and bottom by the GCF 6: 30/36 = 5/6.
| 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 36 | 2 | 36 |
| 3 and 36 | 3 | 36 |
| 4 and 36 | 4 | 36 |
| 5 and 36 | 1 | 180 |
| 6 and 36 | 6 | 36 |
| 7 and 36 | 1 | 252 |
See also: factors of 30 · factors of 36.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.