GCF and LCM of 14 and 26

The GCF of 14 and 26 is 2. The LCM of 14 and 26 is 182.

• GCF (greatest common factor, also called GCD or HCF) of 14 and 26 = 2
• LCM (least common multiple) of 14 and 26 = 182

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
Factors of 26: 1, 2, 13, 26.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

14 = 2 × 7
26 = 2 × 13

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 × 7 × 13 = 182.

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. 26 = 1 × 14 + 12
2. 14 = 1 × 12 + 2
3. 12 = 6 × 2 + 0

The last non-zero remainder is 2, so GCF(14, 26) = 2.

LCM by listing multiples

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, ...
The first number in both lists is 182.

Check: GCF × LCM = product

2 × 182 = 364 = 14 × 26. This always holds for two numbers, so you can find the LCM as (14 × 26) ÷ 2 = 182.

Simplifying the fraction 14/26

Divide the top and bottom by the GCF 2: 14/26 = 7/13.

GCF and LCM of similar pairs

See also: factors of 14 · factors of 26.

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