GCF and LCM of 25 and 48

The GCF of 25 and 48 is 1. The LCM of 25 and 48 is 1,200.

• GCF (greatest common factor, also called GCD or HCF) of 25 and 48 = 1
• LCM (least common multiple) of 25 and 48 = 1,200

25 and 48 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 25 × 48 = 1,200.

Method 1: list the factors (GCF)

Factors of 25: 1, 5, 25.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

25 = 5 × 5
48 = 2 × 2 × 2 × 2 × 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 × 2 × 2 × 3 × 5 × 5 = 1,200.

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. 48 = 1 × 25 + 23
2. 25 = 1 × 23 + 2
3. 23 = 11 × 2 + 1
4. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(25, 48) = 1.

LCM by listing multiples

Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, ...
Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, ...
The first number in both lists is 1,200.

Check: GCF × LCM = product

1 × 1,200 = 1,200 = 25 × 48. This always holds for two numbers, so you can find the LCM as (25 × 48) ÷ 1 = 1,200.

Simplifying the fraction 25/48

25/48 is already in lowest terms because the GCF of 25 and 48 is 1.

GCF and LCM of similar pairs

See also: factors of 25 · factors of 48.

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