GCF and LCM of 14 and 23

The GCF of 14 and 23 is 1. The LCM of 14 and 23 is 322.

• GCF (greatest common factor, also called GCD or HCF) of 14 and 23 = 1
• LCM (least common multiple) of 14 and 23 = 322

14 and 23 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 14 × 23 = 322.

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
Factors of 23: 1, 23.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

14 = 2 × 7
23 = 23 (prime)

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 × 7 × 23 = 322.

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. 23 = 1 × 14 + 9
2. 14 = 1 × 9 + 5
3. 9 = 1 × 5 + 4
4. 5 = 1 × 4 + 1
5. 4 = 4 × 1 + 0

The last non-zero remainder is 1, so GCF(14, 23) = 1.

LCM by listing multiples

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, ...
The first number in both lists is 322.

Check: GCF × LCM = product

1 × 322 = 322 = 14 × 23. This always holds for two numbers, so you can find the LCM as (14 × 23) ÷ 1 = 322.

Simplifying the fraction 14/23

14/23 is already in lowest terms because the GCF of 14 and 23 is 1.

GCF and LCM of similar pairs

See also: factors of 14 · factors of 23.

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