GCF and LCM of 21 and 45

The GCF of 21 and 45 is 3. The LCM of 21 and 45 is 315.

• GCF (greatest common factor, also called GCD or HCF) of 21 and 45 = 3
• LCM (least common multiple) of 21 and 45 = 315

Method 1: list the factors (GCF)

Factors of 21: 1, 3, 7, 21.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1 and 3. The greatest of these is 3.

Method 2: prime factorization

21 = 3 × 7
45 = 3 × 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: 3 × 3 × 5 × 7 = 315.

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. 45 = 2 × 21 + 3
2. 21 = 7 × 3 + 0

The last non-zero remainder is 3, so GCF(21, 45) = 3.

LCM by listing multiples

Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, ...
The first number in both lists is 315.

Check: GCF × LCM = product

3 × 315 = 945 = 21 × 45. This always holds for two numbers, so you can find the LCM as (21 × 45) ÷ 3 = 315.

Simplifying the fraction 21/45

Divide the top and bottom by the GCF 3: 21/45 = 7/15.

GCF and LCM of similar pairs

See also: factors of 21 · factors of 45.

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