GCF and LCM of 10 and 27

The GCF of 10 and 27 is 1. The LCM of 10 and 27 is 270.

• GCF (greatest common factor, also called GCD or HCF) of 10 and 27 = 1
• LCM (least common multiple) of 10 and 27 = 270

10 and 27 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 10 × 27 = 270.

Method 1: list the factors (GCF)

Factors of 10: 1, 2, 5, 10.
Factors of 27: 1, 3, 9, 27.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

10 = 2 × 5
27 = 3 × 3 × 3

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 × 3 × 3 × 3 × 5 = 270.

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. 27 = 2 × 10 + 7
2. 10 = 1 × 7 + 3
3. 7 = 2 × 3 + 1
4. 3 = 3 × 1 + 0

The last non-zero remainder is 1, so GCF(10, 27) = 1.

LCM by listing multiples

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, ...
The first number in both lists is 270.

Check: GCF × LCM = product

1 × 270 = 270 = 10 × 27. This always holds for two numbers, so you can find the LCM as (10 × 27) ÷ 1 = 270.

Simplifying the fraction 10/27

10/27 is already in lowest terms because the GCF of 10 and 27 is 1.

GCF and LCM of similar pairs

See also: factors of 10 · factors of 27.

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