GCF and LCM of 28 and 30

The GCF of 28 and 30 is 2. The LCM of 28 and 30 is 420.

Method 1: list the factors (GCF)

Factors of 28: 1, 2, 4, 7, 14, 28.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

28 = 2 × 2 × 7
30 = 2 × 3 × 5

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 × 3 × 5 × 7 = 420.

Method 3: Euclidean algorithm (GCF)

Divide the larger number by the smaller and repeat with the remainder until it is 0. The last non-zero remainder is the GCF.

  1. 30 = 1 × 28 + 2
  2. 28 = 14 × 2 + 0

The last non-zero remainder is 2, so GCF(28, 30) = 2.

LCM by listing multiples

Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, ...
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, ...
The first number in both lists is 420.

Check: GCF × LCM = product

2 × 420 = 840 = 28 × 30. This always holds for two numbers, so you can find the LCM as (28 × 30) ÷ 2 = 420.

Simplifying the fraction 28/30

Divide the top and bottom by the GCF 2: 28/30 = 14/15.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 28228
3 and 28184
4 and 28428
5 and 281140
6 and 28284
7 and 28728
2 and 30230
3 and 30330
4 and 30260
5 and 30530
6 and 30630
7 and 301210

See also: factors of 28 · factors of 30.

Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.