GCF and LCM of 3 and 14

The GCF of 3 and 14 is 1. The LCM of 3 and 14 is 42.

• GCF (greatest common factor, also called GCD or HCF) of 3 and 14 = 1
• LCM (least common multiple) of 3 and 14 = 42

3 and 14 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 3 × 14 = 42.

Method 1: list the factors (GCF)

Factors of 3: 1, 3.
Factors of 14: 1, 2, 7, 14.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

3 = 3 (prime)
14 = 2 × 7

GCF: multiply the prime factors both numbers share: there are none, so the GCF is 1.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 3 × 7 = 42.

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

The last non-zero remainder is 1, so GCF(3, 14) = 1.

LCM by listing multiples

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, ...
Multiples of 14: 14, 28, 42, 56, ...
The first number in both lists is 42.

Check: GCF × LCM = product

1 × 42 = 42 = 3 × 14. This always holds for two numbers, so you can find the LCM as (3 × 14) ÷ 1 = 42.

Simplifying the fraction 3/14

3/14 is already in lowest terms because the GCF of 3 and 14 is 1.

GCF and LCM of similar pairs

See also: factors of 3 · factors of 14 · 3/14 as a decimal.

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