GCF and LCM of 23 and 48

The GCF of 23 and 48 is 1. The LCM of 23 and 48 is 1,104.

• GCF (greatest common factor, also called GCD or HCF) of 23 and 48 = 1
• LCM (least common multiple) of 23 and 48 = 1,104

23 and 48 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 23 × 48 = 1,104.

Method 1: list the factors (GCF)

Factors of 23: 1, 23.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

23 = 23 (prime)
48 = 2 × 2 × 2 × 2 × 3

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 × 2 × 2 × 2 × 3 × 23 = 1,104.

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. 48 = 2 × 23 + 2
2. 23 = 11 × 2 + 1
3. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(23, 48) = 1.

LCM by listing multiples

Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, ...
Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, ...
The first number in both lists is 1,104.

Check: GCF × LCM = product

1 × 1,104 = 1,104 = 23 × 48. This always holds for two numbers, so you can find the LCM as (23 × 48) ÷ 1 = 1,104.

Simplifying the fraction 23/48

23/48 is already in lowest terms because the GCF of 23 and 48 is 1.

GCF and LCM of similar pairs

See also: factors of 23 · factors of 48.

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