GCF and LCM of 7 and 10

The GCF of 7 and 10 is 1. The LCM of 7 and 10 is 70.

• GCF (greatest common factor, also called GCD or HCF) of 7 and 10 = 1
• LCM (least common multiple) of 7 and 10 = 70

7 and 10 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 7 × 10 = 70.

Method 1: list the factors (GCF)

Factors of 7: 1, 7.
Factors of 10: 1, 2, 5, 10.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

7 = 7 (prime)
10 = 2 × 5

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 × 5 × 7 = 70.

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

The last non-zero remainder is 1, so GCF(7, 10) = 1.

LCM by listing multiples

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, ...
The first number in both lists is 70.

Check: GCF × LCM = product

1 × 70 = 70 = 7 × 10. This always holds for two numbers, so you can find the LCM as (7 × 10) ÷ 1 = 70.

Simplifying the fraction 7/10

7/10 is already in lowest terms because the GCF of 7 and 10 is 1.

GCF and LCM of similar pairs

See also: factors of 7 · factors of 10 · 7/10 as a decimal.

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