GCF and LCM of 29 and 48

The GCF of 29 and 48 is 1. The LCM of 29 and 48 is 1,392.

• GCF (greatest common factor, also called GCD or HCF) of 29 and 48 = 1
• LCM (least common multiple) of 29 and 48 = 1,392

29 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: 29 × 48 = 1,392.

Method 1: list the factors (GCF)

Factors of 29: 1, 29.
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

29 = 29 (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 × 29 = 1,392.

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 = 1 × 29 + 19
2. 29 = 1 × 19 + 10
3. 19 = 1 × 10 + 9
4. 10 = 1 × 9 + 1
5. 9 = 9 × 1 + 0

The last non-zero remainder is 1, so GCF(29, 48) = 1.

LCM by listing multiples

Multiples of 29: 29, 58, 87, 116, 145, 174, 203, 232, 261, ...
Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, ...
The first number in both lists is 1,392.

Check: GCF × LCM = product

1 × 1,392 = 1,392 = 29 × 48. This always holds for two numbers, so you can find the LCM as (29 × 48) ÷ 1 = 1,392.

Simplifying the fraction 29/48

29/48 is already in lowest terms because the GCF of 29 and 48 is 1.

GCF and LCM of similar pairs

See also: factors of 29 · factors of 48.

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