GCF and LCM of 14 and 48

The GCF of 14 and 48 is 2. The LCM of 14 and 48 is 336.

• GCF (greatest common factor, also called GCD or HCF) of 14 and 48 = 2
• LCM (least common multiple) of 14 and 48 = 336

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

14 = 2 × 7
48 = 2 × 2 × 2 × 2 × 3

GCF: multiply the prime factors both numbers share: 2 = 2.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 2 × 3 × 7 = 336.

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 = 3 × 14 + 6
2. 14 = 2 × 6 + 2
3. 6 = 3 × 2 + 0

The last non-zero remainder is 2, so GCF(14, 48) = 2.

LCM by listing multiples

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, ...
The first number in both lists is 336.

Check: GCF × LCM = product

2 × 336 = 672 = 14 × 48. This always holds for two numbers, so you can find the LCM as (14 × 48) ÷ 2 = 336.

Simplifying the fraction 14/48

Divide the top and bottom by the GCF 2: 14/48 = 7/24.

GCF and LCM of similar pairs

See also: factors of 14 · factors of 48.

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