GCF and LCM of 10 and 36

The GCF of 10 and 36 is 2. The LCM of 10 and 36 is 180.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

10 = 2 × 5
36 = 2 × 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 × 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. 36 = 3 × 10 + 6
  2. 10 = 1 × 6 + 4
  3. 6 = 1 × 4 + 2
  4. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(10, 36) = 2.

LCM by listing multiples

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
Multiples of 36: 36, 72, 108, 144, 180, 216, ...
The first number in both lists is 180.

Check: GCF × LCM = product

2 × 180 = 360 = 10 × 36. This always holds for two numbers, so you can find the LCM as (10 × 36) ÷ 2 = 180.

Simplifying the fraction 10/36

Divide the top and bottom by the GCF 2: 10/36 = 5/18.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 10210
3 and 10130
4 and 10220
5 and 10510
6 and 10230
7 and 10170
2 and 36236
3 and 36336
4 and 36436
5 and 361180
6 and 36636
7 and 361252

See also: factors of 10 · factors of 36.

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