GCF and LCM of 14 and 30

The GCF of 14 and 30 is 2. The LCM of 14 and 30 is 210.

• GCF (greatest common factor, also called GCD or HCF) of 14 and 30 = 2
• LCM (least common multiple) of 14 and 30 = 210

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

14 = 2 × 7
30 = 2 × 3 × 5

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 × 3 × 5 × 7 = 210.

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. 30 = 2 × 14 + 2
2. 14 = 7 × 2 + 0

The last non-zero remainder is 2, so GCF(14, 30) = 2.

LCM by listing multiples

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, ...
The first number in both lists is 210.

Check: GCF × LCM = product

2 × 210 = 420 = 14 × 30. This always holds for two numbers, so you can find the LCM as (14 × 30) ÷ 2 = 210.

Simplifying the fraction 14/30

Divide the top and bottom by the GCF 2: 14/30 = 7/15.

GCF and LCM of similar pairs

See also: factors of 14 · factors of 30.

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