GCF and LCM of 9 and 10

The GCF of 9 and 10 is 1. The LCM of 9 and 10 is 90.

9 and 10 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 9 × 10 = 90.

Method 1: list the factors (GCF)

Factors of 9: 1, 3, 9.
Factors of 10: 1, 2, 5, 10.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

9 = 3 × 3
10 = 2 × 5

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 × 3 × 3 × 5 = 90.

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. 10 = 1 × 9 + 1
  2. 9 = 9 × 1 + 0

The last non-zero remainder is 1, so GCF(9, 10) = 1.

LCM by listing multiples

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
The first number in both lists is 90.

Check: GCF × LCM = product

1 × 90 = 90 = 9 × 10. This always holds for two numbers, so you can find the LCM as (9 × 10) ÷ 1 = 90.

Simplifying the fraction 9/10

9/10 is already in lowest terms because the GCF of 9 and 10 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 9118
3 and 939
4 and 9136
5 and 9145
6 and 9318
7 and 9163
2 and 10210
3 and 10130
4 and 10220
5 and 10510
6 and 10230
7 and 10170

See also: factors of 9 · factors of 10 · 9/10 as a decimal.

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