GCF and LCM of 7 and 60

The GCF of 7 and 60 is 1. The LCM of 7 and 60 is 420.

• GCF (greatest common factor, also called GCD or HCF) of 7 and 60 = 1
• LCM (least common multiple) of 7 and 60 = 420

7 and 60 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 7 × 60 = 420.

Method 1: list the factors (GCF)

Factors of 7: 1, 7.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

7 = 7 (prime)
60 = 2 × 2 × 3 × 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 × 3 × 5 × 7 = 420.

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. 60 = 8 × 7 + 4
2. 7 = 1 × 4 + 3
3. 4 = 1 × 3 + 1
4. 3 = 3 × 1 + 0

The last non-zero remainder is 1, so GCF(7, 60) = 1.

LCM by listing multiples

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, ...
The first number in both lists is 420.

Check: GCF × LCM = product

1 × 420 = 420 = 7 × 60. This always holds for two numbers, so you can find the LCM as (7 × 60) ÷ 1 = 420.

Simplifying the fraction 7/60

7/60 is already in lowest terms because the GCF of 7 and 60 is 1.

GCF and LCM of similar pairs

See also: factors of 7 · factors of 60.

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