What is the GCF of 21 and 48?

The greatest common factor of 21 and 48 is 3.

What is the LCM of 21 and 48?

The least common multiple of 21 and 48 is 336.

Are 21 and 48 coprime?

No. They share the common factor 3, and their GCF is 3.

GCF and LCM of 21 and 48

The GCF of 21 and 48 is 3. The LCM of 21 and 48 is 336.

GCF (greatest common factor, also called GCD or HCF) of 21 and 48 = 3
LCM (least common multiple) of 21 and 48 = 336

Method 1: list the factors (GCF)

Factors of 21: 1, 3, 7, 21.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Common factors: 1 and 3. The greatest of these is 3.

Method 2: prime factorization

21 = 3 × 7
48 = 2 × 2 × 2 × 2 × 3

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 × 2 × 2 × 2 × 3 × 7 = 336.

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.

48 = 2 × 21 + 6
21 = 3 × 6 + 3
6 = 2 × 3 + 0

The last non-zero remainder is 3, so GCF(21, 48) = 3.

LCM by listing multiples

Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, ...
The first number in both lists is 336.

Check: GCF × LCM = product

3 × 336 = 1,008 = 21 × 48. This always holds for two numbers, so you can find the LCM as (21 × 48) ÷ 3 = 336.

Simplifying the fraction 21/48

Divide the top and bottom by the GCF 3: 21/48 = 7/16.

GCF and LCM of similar pairs

Numbers	GCF	LCM
2 and 21	1	42
3 and 21	3	21
4 and 21	1	84
5 and 21	1	105
6 and 21	3	42
7 and 21	7	21
2 and 48	2	48
3 and 48	3	48
4 and 48	4	48
5 and 48	1	240
6 and 48	6	48
7 and 48	1	336

See also: factors of 21 · factors of 48.

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