GCF and LCM of 19 and 48

The GCF of 19 and 48 is 1. The LCM of 19 and 48 is 912.

• GCF (greatest common factor, also called GCD or HCF) of 19 and 48 = 1
• LCM (least common multiple) of 19 and 48 = 912

19 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: 19 × 48 = 912.

Method 1: list the factors (GCF)

Factors of 19: 1, 19.
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

19 = 19 (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 × 19 = 912.

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 × 19 + 10
2. 19 = 1 × 10 + 9
3. 10 = 1 × 9 + 1
4. 9 = 9 × 1 + 0

The last non-zero remainder is 1, so GCF(19, 48) = 1.

LCM by listing multiples

Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, ...
Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, ...
The first number in both lists is 912.

Check: GCF × LCM = product

1 × 912 = 912 = 19 × 48. This always holds for two numbers, so you can find the LCM as (19 × 48) ÷ 1 = 912.

Simplifying the fraction 19/48

19/48 is already in lowest terms because the GCF of 19 and 48 is 1.

GCF and LCM of similar pairs

See also: factors of 19 · factors of 48.

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