GCF and LCM of 4 and 14

The GCF of 4 and 14 is 2. The LCM of 4 and 14 is 28.

Method 1: list the factors (GCF)

Factors of 4: 1, 2, 4.
Factors of 14: 1, 2, 7, 14.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

4 = 2 × 2
14 = 2 × 7

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 × 7 = 28.

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. 14 = 3 × 4 + 2
  2. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(4, 14) = 2.

LCM by listing multiples

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
Multiples of 14: 14, 28, 42, ...
The first number in both lists is 28.

Check: GCF × LCM = product

2 × 28 = 56 = 4 × 14. This always holds for two numbers, so you can find the LCM as (4 × 14) ÷ 2 = 28.

Simplifying the fraction 4/14

Divide the top and bottom by the GCF 2: 4/14 = 2/7.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 424
3 and 4112
4 and 5120
4 and 6212
4 and 7128
4 and 848
2 and 14214
3 and 14142
5 and 14170
6 and 14242
7 and 14714
8 and 14256

See also: factors of 4 · factors of 14 · 4/14 as a decimal.

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