GCF and LCM of 25 and 45

The GCF of 25 and 45 is 5. The LCM of 25 and 45 is 225.

• GCF (greatest common factor, also called GCD or HCF) of 25 and 45 = 5
• LCM (least common multiple) of 25 and 45 = 225

Method 1: list the factors (GCF)

Factors of 25: 1, 5, 25.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1 and 5. The greatest of these is 5.

Method 2: prime factorization

25 = 5 × 5
45 = 3 × 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: 3 × 3 × 5 × 5 = 225.

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. 45 = 1 × 25 + 20
2. 25 = 1 × 20 + 5
3. 20 = 4 × 5 + 0

The last non-zero remainder is 5, so GCF(25, 45) = 5.

LCM by listing multiples

Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, ...
Multiples of 45: 45, 90, 135, 180, 225, 270, ...
The first number in both lists is 225.

Check: GCF × LCM = product

5 × 225 = 1,125 = 25 × 45. This always holds for two numbers, so you can find the LCM as (25 × 45) ÷ 5 = 225.

Simplifying the fraction 25/45

Divide the top and bottom by the GCF 5: 25/45 = 5/9.

GCF and LCM of similar pairs

See also: factors of 25 · factors of 45.

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