GCF and LCM of 14 and 28

The GCF of 14 and 28 is 14. The LCM of 14 and 28 is 28.

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
Factors of 28: 1, 2, 4, 7, 14, 28.
Common factors: 1, 2, 7 and 14. The greatest of these is 14.

Method 2: prime factorization

14 = 2 × 7
28 = 2 × 2 × 7

GCF: multiply the prime factors both numbers share: 2 × 7 = 14.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 7 = 28.

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. 28 = 2 × 14 + 0

The last non-zero remainder is 14, so GCF(14, 28) = 14.

LCM by listing multiples

Multiples of 14: 14, 28, 42, ...
Multiples of 28: 28, 56, ...
The first number in both lists is 28.

Check: GCF × LCM = product

14 × 28 = 392 = 14 × 28. This always holds for two numbers, so you can find the LCM as (14 × 28) ÷ 14 = 28.

Simplifying the fraction 14/28

Divide the top and bottom by the GCF 14: 14/28 = 1/2.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 14214
3 and 14142
4 and 14228
5 and 14170
6 and 14242
7 and 14714
2 and 28228
3 and 28184
4 and 28428
5 and 281140
6 and 28284
7 and 28728

See also: factors of 14 · factors of 28.

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