GCF and LCM of 14 and 24

The GCF of 14 and 24 is 2. The LCM of 14 and 24 is 168.

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

14 = 2 × 7
24 = 2 × 2 × 2 × 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 × 2 × 3 × 7 = 168.

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. 24 = 1 × 14 + 10
  2. 14 = 1 × 10 + 4
  3. 10 = 2 × 4 + 2
  4. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(14, 24) = 2.

LCM by listing multiples

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, ...
The first number in both lists is 168.

Check: GCF × LCM = product

2 × 168 = 336 = 14 × 24. This always holds for two numbers, so you can find the LCM as (14 × 24) ÷ 2 = 168.

Simplifying the fraction 14/24

Divide the top and bottom by the GCF 2: 14/24 = 7/12.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 14214
3 and 14142
4 and 14228
5 and 14170
6 and 14242
7 and 14714
2 and 24224
3 and 24324
4 and 24424
5 and 241120
6 and 24624
7 and 241168

See also: factors of 14 · factors of 24.

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