GCF and LCM of 7 and 40

The GCF of 7 and 40 is 1. The LCM of 7 and 40 is 280.

• GCF (greatest common factor, also called GCD or HCF) of 7 and 40 = 1
• LCM (least common multiple) of 7 and 40 = 280

7 and 40 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 7 × 40 = 280.

Method 1: list the factors (GCF)

Factors of 7: 1, 7.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

7 = 7 (prime)
40 = 2 × 2 × 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 × 2 × 2 × 5 × 7 = 280.

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. 40 = 5 × 7 + 5
2. 7 = 1 × 5 + 2
3. 5 = 2 × 2 + 1
4. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(7, 40) = 1.

LCM by listing multiples

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, ...
The first number in both lists is 280.

Check: GCF × LCM = product

1 × 280 = 280 = 7 × 40. This always holds for two numbers, so you can find the LCM as (7 × 40) ÷ 1 = 280.

Simplifying the fraction 7/40

7/40 is already in lowest terms because the GCF of 7 and 40 is 1.

GCF and LCM of similar pairs

See also: factors of 7 · factors of 40 · 7/40 as a decimal.

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