GCF and LCM of 26 and 36

The GCF of 26 and 36 is 2. The LCM of 26 and 36 is 468.

• GCF (greatest common factor, also called GCD or HCF) of 26 and 36 = 2
• LCM (least common multiple) of 26 and 36 = 468

Method 1: list the factors (GCF)

Factors of 26: 1, 2, 13, 26.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

26 = 2 × 13
36 = 2 × 2 × 3 × 3

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 × 2 × 3 × 3 × 13 = 468.

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. 36 = 1 × 26 + 10
2. 26 = 2 × 10 + 6
3. 10 = 1 × 6 + 4
4. 6 = 1 × 4 + 2
5. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(26, 36) = 2.

LCM by listing multiples

Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, ...
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, ...
The first number in both lists is 468.

Check: GCF × LCM = product

2 × 468 = 936 = 26 × 36. This always holds for two numbers, so you can find the LCM as (26 × 36) ÷ 2 = 468.

Simplifying the fraction 26/36

Divide the top and bottom by the GCF 2: 26/36 = 13/18.

GCF and LCM of similar pairs

See also: factors of 26 · factors of 36.

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