GCF and LCM of 10 and 29

The GCF of 10 and 29 is 1. The LCM of 10 and 29 is 290.

10 and 29 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 10 × 29 = 290.

Method 1: list the factors (GCF)

Factors of 10: 1, 2, 5, 10.
Factors of 29: 1, 29.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

10 = 2 × 5
29 = 29 (prime)

GCF: multiply the prime factors both numbers share: there are none, so the GCF is 1.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 5 × 29 = 290.

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. 29 = 2 × 10 + 9
  2. 10 = 1 × 9 + 1
  3. 9 = 9 × 1 + 0

The last non-zero remainder is 1, so GCF(10, 29) = 1.

LCM by listing multiples

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
Multiples of 29: 29, 58, 87, 116, 145, 174, 203, 232, 261, ...
The first number in both lists is 290.

Check: GCF × LCM = product

1 × 290 = 290 = 10 × 29. This always holds for two numbers, so you can find the LCM as (10 × 29) ÷ 1 = 290.

Simplifying the fraction 10/29

10/29 is already in lowest terms because the GCF of 10 and 29 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 10210
3 and 10130
4 and 10220
5 and 10510
6 and 10230
7 and 10170
2 and 29158
3 and 29187
4 and 291116
5 and 291145
6 and 291174
7 and 291203

See also: factors of 10 · factors of 29.

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