GCF and LCM of 60 and 100

The GCF of 60 and 100 is 20. The LCM of 60 and 100 is 300.

Method 1: list the factors (GCF)

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1, 2, 4, 5, 10 and 20. The greatest of these is 20.

Method 2: prime factorization

60 = 2 × 2 × 3 × 5
100 = 2 × 2 × 5 × 5

GCF: multiply the prime factors both numbers share: 2 × 2 × 5 = 20.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 5 × 5 = 300.

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 = 1 × 60 + 40
  2. 60 = 1 × 40 + 20
  3. 40 = 2 × 20 + 0

The last non-zero remainder is 20, so GCF(60, 100) = 20.

LCM by listing multiples

Multiples of 60: 60, 120, 180, 240, 300, 360, ...
Multiples of 100: 100, 200, 300, 400, ...
The first number in both lists is 300.

Check: GCF × LCM = product

20 × 300 = 6,000 = 60 × 100. This always holds for two numbers, so you can find the LCM as (60 × 100) ÷ 20 = 300.

Simplifying the fraction 60/100

Divide the top and bottom by the GCF 20: 60/100 = 3/5.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 60260
3 and 60360
4 and 60460
5 and 60560
6 and 60660
7 and 601420
2 and 1002100
3 and 1001300
4 and 1004100
5 and 1005100
6 and 1002300
7 and 1001700

See also: factors of 60 · factors of 100.

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