GCF and LCM of 40 and 48

The GCF of 40 and 48 is 8. The LCM of 40 and 48 is 240.

Method 1: list the factors (GCF)

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Common factors: 1, 2, 4 and 8. The greatest of these is 8.

Method 2: prime factorization

40 = 2 × 2 × 2 × 5
48 = 2 × 2 × 2 × 2 × 3

GCF: multiply the prime factors both numbers share: 2 × 2 × 2 = 8.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 2 × 3 × 5 = 240.

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. 48 = 1 × 40 + 8
  2. 40 = 5 × 8 + 0

The last non-zero remainder is 8, so GCF(40, 48) = 8.

LCM by listing multiples

Multiples of 40: 40, 80, 120, 160, 200, 240, 280, ...
Multiples of 48: 48, 96, 144, 192, 240, 288, ...
The first number in both lists is 240.

Check: GCF × LCM = product

8 × 240 = 1,920 = 40 × 48. This always holds for two numbers, so you can find the LCM as (40 × 48) ÷ 8 = 240.

Simplifying the fraction 40/48

Divide the top and bottom by the GCF 8: 40/48 = 5/6.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 40240
3 and 401120
4 and 40440
5 and 40540
6 and 402120
7 and 401280
2 and 48248
3 and 48348
4 and 48448
5 and 481240
6 and 48648
7 and 481336

See also: factors of 40 · factors of 48.

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