GCF and LCM of 14 and 19

The GCF of 14 and 19 is 1. The LCM of 14 and 19 is 266.

14 and 19 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 14 × 19 = 266.

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
Factors of 19: 1, 19.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

14 = 2 × 7
19 = 19 (prime)

GCF: multiply the prime factors both numbers share: there are none, so the GCF is 1.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 7 × 19 = 266.

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. 19 = 1 × 14 + 5
  2. 14 = 2 × 5 + 4
  3. 5 = 1 × 4 + 1
  4. 4 = 4 × 1 + 0

The last non-zero remainder is 1, so GCF(14, 19) = 1.

LCM by listing multiples

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, ...
The first number in both lists is 266.

Check: GCF × LCM = product

1 × 266 = 266 = 14 × 19. This always holds for two numbers, so you can find the LCM as (14 × 19) ÷ 1 = 266.

Simplifying the fraction 14/19

14/19 is already in lowest terms because the GCF of 14 and 19 is 1.

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 19138
3 and 19157
4 and 19176
5 and 19195
6 and 191114
7 and 191133

See also: factors of 14 · factors of 19 · 14/19 as a decimal.

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