GCF and LCM of 18 and 26

The GCF of 18 and 26 is 2. The LCM of 18 and 26 is 234.

• GCF (greatest common factor, also called GCD or HCF) of 18 and 26 = 2
• LCM (least common multiple) of 18 and 26 = 234

Method 1: list the factors (GCF)

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

Method 2: prime factorization

18 = 2 × 3 × 3
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 × 3 × 3 × 13 = 234.

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 × 18 + 8
2. 18 = 2 × 8 + 2
3. 8 = 4 × 2 + 0

The last non-zero remainder is 2, so GCF(18, 26) = 2.

LCM by listing multiples

Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, ...
Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, ...
The first number in both lists is 234.

Check: GCF × LCM = product

2 × 234 = 468 = 18 × 26. This always holds for two numbers, so you can find the LCM as (18 × 26) ÷ 2 = 234.

Simplifying the fraction 18/26

Divide the top and bottom by the GCF 2: 18/26 = 9/13.

GCF and LCM of similar pairs

See also: factors of 18 · factors of 26.

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