GCF and LCM of 36 and 100

The GCF of 36 and 100 is 4. The LCM of 36 and 100 is 900.

Method 1: list the factors (GCF)

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1, 2 and 4. The greatest of these is 4.

Method 2: prime factorization

36 = 2 × 2 × 3 × 3
100 = 2 × 2 × 5 × 5

GCF: multiply the prime factors both numbers share: 2 × 2 = 4.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 3 × 5 × 5 = 900.

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 = 2 × 36 + 28
  2. 36 = 1 × 28 + 8
  3. 28 = 3 × 8 + 4
  4. 8 = 2 × 4 + 0

The last non-zero remainder is 4, so GCF(36, 100) = 4.

LCM by listing multiples

Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, ...
Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, ...
The first number in both lists is 900.

Check: GCF × LCM = product

4 × 900 = 3,600 = 36 × 100. This always holds for two numbers, so you can find the LCM as (36 × 100) ÷ 4 = 900.

Simplifying the fraction 36/100

Divide the top and bottom by the GCF 4: 36/100 = 9/25.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 36236
3 and 36336
4 and 36436
5 and 361180
6 and 36636
7 and 361252
2 and 1002100
3 and 1001300
4 and 1004100
5 and 1005100
6 and 1002300
7 and 1001700

See also: factors of 36 · factors of 100.

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