GCF and LCM of 26 and 50

The GCF of 26 and 50 is 2. The LCM of 26 and 50 is 650.

Method 1: list the factors (GCF)

Factors of 26: 1, 2, 13, 26.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

26 = 2 × 13
50 = 2 × 5 × 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 × 5 × 5 × 13 = 650.

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. 50 = 1 × 26 + 24
  2. 26 = 1 × 24 + 2
  3. 24 = 12 × 2 + 0

The last non-zero remainder is 2, so GCF(26, 50) = 2.

LCM by listing multiples

Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, ...
The first number in both lists is 650.

Check: GCF × LCM = product

2 × 650 = 1,300 = 26 × 50. This always holds for two numbers, so you can find the LCM as (26 × 50) ÷ 2 = 650.

Simplifying the fraction 26/50

Divide the top and bottom by the GCF 2: 26/50 = 13/25.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 26226
3 and 26178
4 and 26252
5 and 261130
6 and 26278
7 and 261182
2 and 50250
3 and 501150
4 and 502100
5 and 50550
6 and 502150
7 and 501350

See also: factors of 26 · factors of 50.

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