GCF and LCM of 16 and 18

The GCF of 16 and 18 is 2. The LCM of 16 and 18 is 144.

Method 1: list the factors (GCF)

Factors of 16: 1, 2, 4, 8, 16.
Factors of 18: 1, 2, 3, 6, 9, 18.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

16 = 2 × 2 × 2 × 2
18 = 2 × 3 × 3

GCF: multiply the prime factors both numbers share: 2 = 2.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 2 × 3 × 3 = 144.

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. 18 = 1 × 16 + 2
  2. 16 = 8 × 2 + 0

The last non-zero remainder is 2, so GCF(16, 18) = 2.

LCM by listing multiples

Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ...
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, ...
The first number in both lists is 144.

Check: GCF × LCM = product

2 × 144 = 288 = 16 × 18. This always holds for two numbers, so you can find the LCM as (16 × 18) ÷ 2 = 144.

Simplifying the fraction 16/18

Divide the top and bottom by the GCF 2: 16/18 = 8/9.

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 18218
3 and 18318
4 and 18236
5 and 18190
6 and 18618
7 and 181126

See also: factors of 16 · factors of 18 · 16/18 as a decimal.

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