GCF and LCM of 26 and 29

The GCF of 26 and 29 is 1. The LCM of 26 and 29 is 754.

• GCF (greatest common factor, also called GCD or HCF) of 26 and 29 = 1
• LCM (least common multiple) of 26 and 29 = 754

26 and 29 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 26 × 29 = 754.

Method 1: list the factors (GCF)

Factors of 26: 1, 2, 13, 26.
Factors of 29: 1, 29.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

26 = 2 × 13
29 = 29 (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 × 13 × 29 = 754.

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. 29 = 1 × 26 + 3
2. 26 = 8 × 3 + 2
3. 3 = 1 × 2 + 1
4. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(26, 29) = 1.

LCM by listing multiples

Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, ...
Multiples of 29: 29, 58, 87, 116, 145, 174, 203, 232, 261, ...
The first number in both lists is 754.

Check: GCF × LCM = product

1 × 754 = 754 = 26 × 29. This always holds for two numbers, so you can find the LCM as (26 × 29) ÷ 1 = 754.

Simplifying the fraction 26/29

26/29 is already in lowest terms because the GCF of 26 and 29 is 1.

GCF and LCM of similar pairs

See also: factors of 26 · factors of 29.

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