GCF and LCM of 3 and 100

The GCF of 3 and 100 is 1. The LCM of 3 and 100 is 300.

3 and 100 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 3 × 100 = 300.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

3 = 3 (prime)
100 = 2 × 2 × 5 × 5

GCF: multiply the prime factors both numbers share: there are none, so the GCF is 1.

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 = 33 × 3 + 1
  2. 3 = 3 × 1 + 0

The last non-zero remainder is 1, so GCF(3, 100) = 1.

LCM by listing multiples

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, ...
Multiples of 100: 100, 200, 300, 400, ...
The first number in both lists is 300.

Check: GCF × LCM = product

1 × 300 = 300 = 3 × 100. This always holds for two numbers, so you can find the LCM as (3 × 100) ÷ 1 = 300.

Simplifying the fraction 3/100

3/100 is already in lowest terms because the GCF of 3 and 100 is 1.

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 1002100
4 and 1004100
5 and 1005100
6 and 1002300
7 and 1001700
8 and 1004200

See also: factors of 3 · factors of 100.

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