GCF and LCM of 3 and 30

The GCF of 3 and 30 is 3. The LCM of 3 and 30 is 30.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

3 = 3 (prime)
30 = 2 × 3 × 5

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

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 3 × 5 = 30.

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 = 10 × 3 + 0

The last non-zero remainder is 3, so GCF(3, 30) = 3.

LCM by listing multiples

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, ...
Multiples of 30: 30, 60, ...
The first number in both lists is 30.

Check: GCF × LCM = product

3 × 30 = 90 = 3 × 30. This always holds for two numbers, so you can find the LCM as (3 × 30) ÷ 3 = 30.

Simplifying the fraction 3/30

Divide the top and bottom by the GCF 3: 3/30 = 1/10.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 316
3 and 4112
3 and 5115
3 and 636
3 and 7121
3 and 8124
2 and 30230
4 and 30260
5 and 30530
6 and 30630
7 and 301210
8 and 302120

See also: factors of 3 · factors of 30.

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