GCF and LCM of 30 and 48

The GCF of 30 and 48 is 6. The LCM of 30 and 48 is 240.

• GCF (greatest common factor, also called GCD or HCF) of 30 and 48 = 6
• LCM (least common multiple) of 30 and 48 = 240

Method 1: list the factors (GCF)

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Common factors: 1, 2, 3 and 6. The greatest of these is 6.

Method 2: prime factorization

30 = 2 × 3 × 5
48 = 2 × 2 × 2 × 2 × 3

GCF: multiply the prime factors both numbers share: 2 × 3 = 6.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 2 × 3 × 5 = 240.

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 × 30 + 18
2. 30 = 1 × 18 + 12
3. 18 = 1 × 12 + 6
4. 12 = 2 × 6 + 0

The last non-zero remainder is 6, so GCF(30, 48) = 6.

LCM by listing multiples

Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, ...
Multiples of 48: 48, 96, 144, 192, 240, 288, ...
The first number in both lists is 240.

Check: GCF × LCM = product

6 × 240 = 1,440 = 30 × 48. This always holds for two numbers, so you can find the LCM as (30 × 48) ÷ 6 = 240.

Simplifying the fraction 30/48

Divide the top and bottom by the GCF 6: 30/48 = 5/8.

GCF and LCM of similar pairs

See also: factors of 30 · factors of 48.

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