GCF and LCM of 8 and 21

The GCF of 8 and 21 is 1. The LCM of 8 and 21 is 168.

• GCF (greatest common factor, also called GCD or HCF) of 8 and 21 = 1
• LCM (least common multiple) of 8 and 21 = 168

8 and 21 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 8 × 21 = 168.

Method 1: list the factors (GCF)

Factors of 8: 1, 2, 4, 8.
Factors of 21: 1, 3, 7, 21.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

8 = 2 × 2 × 2
21 = 3 × 7

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 × 2 × 3 × 7 = 168.

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. 21 = 2 × 8 + 5
2. 8 = 1 × 5 + 3
3. 5 = 1 × 3 + 2
4. 3 = 1 × 2 + 1
5. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(8, 21) = 1.

LCM by listing multiples

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
The first number in both lists is 168.

Check: GCF × LCM = product

1 × 168 = 168 = 8 × 21. This always holds for two numbers, so you can find the LCM as (8 × 21) ÷ 1 = 168.

Simplifying the fraction 8/21

8/21 is already in lowest terms because the GCF of 8 and 21 is 1.

GCF and LCM of similar pairs

See also: factors of 8 · factors of 21.

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