GCF and LCM of 30 and 100

The GCF of 30 and 100 is 10. The LCM of 30 and 100 is 300.

• GCF (greatest common factor, also called GCD or HCF) of 30 and 100 = 10
• LCM (least common multiple) of 30 and 100 = 300

Method 1: list the factors (GCF)

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1, 2, 5 and 10. The greatest of these is 10.

Method 2: prime factorization

30 = 2 × 3 × 5
100 = 2 × 2 × 5 × 5

GCF: multiply the prime factors both numbers share: 2 × 5 = 10.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 5 × 5 = 300.

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. 100 = 3 × 30 + 10
2. 30 = 3 × 10 + 0

The last non-zero remainder is 10, so GCF(30, 100) = 10.

LCM by listing multiples

Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, ...
Multiples of 100: 100, 200, 300, 400, ...
The first number in both lists is 300.

Check: GCF × LCM = product

10 × 300 = 3,000 = 30 × 100. This always holds for two numbers, so you can find the LCM as (30 × 100) ÷ 10 = 300.

Simplifying the fraction 30/100

Divide the top and bottom by the GCF 10: 30/100 = 3/10.

GCF and LCM of similar pairs

See also: factors of 30 · factors of 100.

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