GCF and LCM of 40 and 60

The GCF of 40 and 60 is 20. The LCM of 40 and 60 is 120.

Method 1: list the factors (GCF)

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1, 2, 4, 5, 10 and 20. The greatest of these is 20.

Method 2: prime factorization

40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 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 × 2 × 3 × 5 = 120.

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 × 40 + 20
  2. 40 = 2 × 20 + 0

The last non-zero remainder is 20, so GCF(40, 60) = 20.

LCM by listing multiples

Multiples of 40: 40, 80, 120, 160, ...
Multiples of 60: 60, 120, 180, ...
The first number in both lists is 120.

Check: GCF × LCM = product

20 × 120 = 2,400 = 40 × 60. This always holds for two numbers, so you can find the LCM as (40 × 60) ÷ 20 = 120.

Simplifying the fraction 40/60

Divide the top and bottom by the GCF 20: 40/60 = 2/3.

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

See also: factors of 40 · factors of 60.

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