GCF and LCM of 4 and 21

The GCF of 4 and 21 is 1. The LCM of 4 and 21 is 84.

• GCF (greatest common factor, also called GCD or HCF) of 4 and 21 = 1
• LCM (least common multiple) of 4 and 21 = 84

4 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: 4 × 21 = 84.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

4 = 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 × 3 × 7 = 84.

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 = 5 × 4 + 1
2. 4 = 4 × 1 + 0

The last non-zero remainder is 1, so GCF(4, 21) = 1.

LCM by listing multiples

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Multiples of 21: 21, 42, 63, 84, 105, ...
The first number in both lists is 84.

Check: GCF × LCM = product

1 × 84 = 84 = 4 × 21. This always holds for two numbers, so you can find the LCM as (4 × 21) ÷ 1 = 84.

Simplifying the fraction 4/21

4/21 is already in lowest terms because the GCF of 4 and 21 is 1.

GCF and LCM of similar pairs

See also: factors of 4 · factors of 21.

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