GCF and LCM of 16 and 45

The GCF of 16 and 45 is 1. The LCM of 16 and 45 is 720.

16 and 45 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 16 × 45 = 720.

Method 1: list the factors (GCF)

Factors of 16: 1, 2, 4, 8, 16.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

16 = 2 × 2 × 2 × 2
45 = 3 × 3 × 5

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 × 3 × 5 = 720.

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 × 16 + 13
  2. 16 = 1 × 13 + 3
  3. 13 = 4 × 3 + 1
  4. 3 = 3 × 1 + 0

The last non-zero remainder is 1, so GCF(16, 45) = 1.

LCM by listing multiples

Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ...
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...
The first number in both lists is 720.

Check: GCF × LCM = product

1 × 720 = 720 = 16 × 45. This always holds for two numbers, so you can find the LCM as (16 × 45) ÷ 1 = 720.

Simplifying the fraction 16/45

16/45 is already in lowest terms because the GCF of 16 and 45 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 16216
3 and 16148
4 and 16416
5 and 16180
6 and 16248
7 and 161112
2 and 45190
3 and 45345
4 and 451180
5 and 45545
6 and 45390
7 and 451315

See also: factors of 16 · factors of 45.

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