GCF and LCM of 25 and 100

The GCF of 25 and 100 is 25. The LCM of 25 and 100 is 100.

Method 1: list the factors (GCF)

Factors of 25: 1, 5, 25.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1, 5 and 25. The greatest of these is 25.

Method 2: prime factorization

25 = 5 × 5
100 = 2 × 2 × 5 × 5

GCF: multiply the prime factors both numbers share: 5 × 5 = 25.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 5 × 5 = 100.

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. 100 = 4 × 25 + 0

The last non-zero remainder is 25, so GCF(25, 100) = 25.

LCM by listing multiples

Multiples of 25: 25, 50, 75, 100, 125, ...
Multiples of 100: 100, 200, ...
The first number in both lists is 100.

Check: GCF × LCM = product

25 × 100 = 2,500 = 25 × 100. This always holds for two numbers, so you can find the LCM as (25 × 100) ÷ 25 = 100.

Simplifying the fraction 25/100

Divide the top and bottom by the GCF 25: 25/100 = 1/4.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 25150
3 and 25175
4 and 251100
5 and 25525
6 and 251150
7 and 251175
2 and 1002100
3 and 1001300
4 and 1004100
5 and 1005100
6 and 1002300
7 and 1001700

See also: factors of 25 · factors of 100.

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