GCF and LCM of 25 and 36

The GCF of 25 and 36 is 1. The LCM of 25 and 36 is 900.

• GCF (greatest common factor, also called GCD or HCF) of 25 and 36 = 1
• LCM (least common multiple) of 25 and 36 = 900

25 and 36 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 25 × 36 = 900.

Method 1: list the factors (GCF)

Factors of 25: 1, 5, 25.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

25 = 5 × 5
36 = 2 × 2 × 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 × 2 × 3 × 3 × 5 × 5 = 900.

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. 36 = 1 × 25 + 11
2. 25 = 2 × 11 + 3
3. 11 = 3 × 3 + 2
4. 3 = 1 × 2 + 1
5. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(25, 36) = 1.

LCM by listing multiples

Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, ...
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, ...
The first number in both lists is 900.

Check: GCF × LCM = product

1 × 900 = 900 = 25 × 36. This always holds for two numbers, so you can find the LCM as (25 × 36) ÷ 1 = 900.

Simplifying the fraction 25/36

25/36 is already in lowest terms because the GCF of 25 and 36 is 1.

GCF and LCM of similar pairs

See also: factors of 25 · factors of 36.

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