GCF and LCM of 25 and 60

The GCF of 25 and 60 is 5. The LCM of 25 and 60 is 300.

• GCF (greatest common factor, also called GCD or HCF) of 25 and 60 = 5
• LCM (least common multiple) of 25 and 60 = 300

Method 1: list the factors (GCF)

Factors of 25: 1, 5, 25.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1 and 5. The greatest of these is 5.

Method 2: prime factorization

25 = 5 × 5
60 = 2 × 2 × 3 × 5

GCF: multiply the prime factors both numbers share: 5 = 5.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 5 × 5 = 300.

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 = 2 × 25 + 10
2. 25 = 2 × 10 + 5
3. 10 = 2 × 5 + 0

The last non-zero remainder is 5, so GCF(25, 60) = 5.

LCM by listing multiples

Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, ...
Multiples of 60: 60, 120, 180, 240, 300, 360, ...
The first number in both lists is 300.

Check: GCF × LCM = product

5 × 300 = 1,500 = 25 × 60. This always holds for two numbers, so you can find the LCM as (25 × 60) ÷ 5 = 300.

Simplifying the fraction 25/60

Divide the top and bottom by the GCF 5: 25/60 = 5/12.

GCF and LCM of similar pairs

See also: factors of 25 · factors of 60.

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