GCF and LCM of 14 and 16

The GCF of 14 and 16 is 2. The LCM of 14 and 16 is 112.

• GCF (greatest common factor, also called GCD or HCF) of 14 and 16 = 2
• LCM (least common multiple) of 14 and 16 = 112

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
Factors of 16: 1, 2, 4, 8, 16.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

14 = 2 × 7
16 = 2 × 2 × 2 × 2

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 × 2 × 2 × 7 = 112.

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. 16 = 1 × 14 + 2
2. 14 = 7 × 2 + 0

The last non-zero remainder is 2, so GCF(14, 16) = 2.

LCM by listing multiples

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, ...
The first number in both lists is 112.

Check: GCF × LCM = product

2 × 112 = 224 = 14 × 16. This always holds for two numbers, so you can find the LCM as (14 × 16) ÷ 2 = 112.

Simplifying the fraction 14/16

Divide the top and bottom by the GCF 2: 14/16 = 7/8.

GCF and LCM of similar pairs

See also: factors of 14 · factors of 16 · 14/16 as a decimal.

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