GCF and LCM of 14 and 36

The GCF of 14 and 36 is 2. The LCM of 14 and 36 is 252.

• GCF (greatest common factor, also called GCD or HCF) of 14 and 36 = 2
• LCM (least common multiple) of 14 and 36 = 252

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
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

14 = 2 × 7
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 × 7 = 252.

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 = 2 × 14 + 8
2. 14 = 1 × 8 + 6
3. 8 = 1 × 6 + 2
4. 6 = 3 × 2 + 0

The last non-zero remainder is 2, so GCF(14, 36) = 2.

LCM by listing multiples

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, ...
The first number in both lists is 252.

Check: GCF × LCM = product

2 × 252 = 504 = 14 × 36. This always holds for two numbers, so you can find the LCM as (14 × 36) ÷ 2 = 252.

Simplifying the fraction 14/36

Divide the top and bottom by the GCF 2: 14/36 = 7/18.

GCF and LCM of similar pairs

See also: factors of 14 · factors of 36.

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