GCF and LCM of 15 and 23

The GCF of 15 and 23 is 1. The LCM of 15 and 23 is 345.

• GCF (greatest common factor, also called GCD or HCF) of 15 and 23 = 1
• LCM (least common multiple) of 15 and 23 = 345

15 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: 15 × 23 = 345.

Method 1: list the factors (GCF)

Factors of 15: 1, 3, 5, 15.
Factors of 23: 1, 23.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

15 = 3 × 5
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: 3 × 5 × 23 = 345.

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 × 15 + 8
2. 15 = 1 × 8 + 7
3. 8 = 1 × 7 + 1
4. 7 = 7 × 1 + 0

The last non-zero remainder is 1, so GCF(15, 23) = 1.

LCM by listing multiples

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, ...
Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, ...
The first number in both lists is 345.

Check: GCF × LCM = product

1 × 345 = 345 = 15 × 23. This always holds for two numbers, so you can find the LCM as (15 × 23) ÷ 1 = 345.

Simplifying the fraction 15/23

15/23 is already in lowest terms because the GCF of 15 and 23 is 1.

GCF and LCM of similar pairs

See also: factors of 15 · factors of 23.

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