GCF and LCM of 36 and 60

The GCF of 36 and 60 is 12. The LCM of 36 and 60 is 180.

Method 1: list the factors (GCF)

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1, 2, 3, 4, 6 and 12. The greatest of these is 12.

Method 2: prime factorization

36 = 2 × 2 × 3 × 3
60 = 2 × 2 × 3 × 5

GCF: multiply the prime factors both numbers share: 2 × 2 × 3 = 12.

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. 60 = 1 × 36 + 24
  2. 36 = 1 × 24 + 12
  3. 24 = 2 × 12 + 0

The last non-zero remainder is 12, so GCF(36, 60) = 12.

LCM by listing multiples

Multiples of 36: 36, 72, 108, 144, 180, 216, ...
Multiples of 60: 60, 120, 180, 240, ...
The first number in both lists is 180.

Check: GCF × LCM = product

12 × 180 = 2,160 = 36 × 60. This always holds for two numbers, so you can find the LCM as (36 × 60) ÷ 12 = 180.

Simplifying the fraction 36/60

Divide the top and bottom by the GCF 12: 36/60 = 3/5.

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 60260
3 and 60360
4 and 60460
5 and 60560
6 and 60660
7 and 601420

See also: factors of 36 · factors of 60.

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