GCF and LCM of 20 and 45

The GCF of 20 and 45 is 5. The LCM of 20 and 45 is 180.

Method 1: list the factors (GCF)

Factors of 20: 1, 2, 4, 5, 10, 20.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1 and 5. The greatest of these is 5.

Method 2: prime factorization

20 = 2 × 2 × 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: 2 × 2 × 3 × 3 × 5 = 180.

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 = 2 × 20 + 5
  2. 20 = 4 × 5 + 0

The last non-zero remainder is 5, so GCF(20, 45) = 5.

LCM by listing multiples

Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, ...
Multiples of 45: 45, 90, 135, 180, 225, ...
The first number in both lists is 180.

Check: GCF × LCM = product

5 × 180 = 900 = 20 × 45. This always holds for two numbers, so you can find the LCM as (20 × 45) ÷ 5 = 180.

Simplifying the fraction 20/45

Divide the top and bottom by the GCF 5: 20/45 = 4/9.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 20220
3 and 20160
4 and 20420
5 and 20520
6 and 20260
7 and 201140
2 and 45190
3 and 45345
4 and 451180
5 and 45545
6 and 45390
7 and 451315

See also: factors of 20 · factors of 45.

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