GCF and LCM of 22 and 100

The GCF of 22 and 100 is 2. The LCM of 22 and 100 is 1,100.

Method 1: list the factors (GCF)

Factors of 22: 1, 2, 11, 22.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

22 = 2 × 11
100 = 2 × 2 × 5 × 5

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 × 5 × 5 × 11 = 1,100.

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 × 22 + 12
  2. 22 = 1 × 12 + 10
  3. 12 = 1 × 10 + 2
  4. 10 = 5 × 2 + 0

The last non-zero remainder is 2, so GCF(22, 100) = 2.

LCM by listing multiples

Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, ...
Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, ...
The first number in both lists is 1,100.

Check: GCF × LCM = product

2 × 1,100 = 2,200 = 22 × 100. This always holds for two numbers, so you can find the LCM as (22 × 100) ÷ 2 = 1,100.

Simplifying the fraction 22/100

Divide the top and bottom by the GCF 2: 22/100 = 11/50.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 22222
3 and 22166
4 and 22244
5 and 221110
6 and 22266
7 and 221154
2 and 1002100
3 and 1001300
4 and 1004100
5 and 1005100
6 and 1002300
7 and 1001700

See also: factors of 22 · factors of 100.

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