GCF and LCM of 17 and 30

The GCF of 17 and 30 is 1. The LCM of 17 and 30 is 510.

17 and 30 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 17 × 30 = 510.

Method 1: list the factors (GCF)

Factors of 17: 1, 17.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

17 = 17 (prime)
30 = 2 × 3 × 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 × 5 × 17 = 510.

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. 30 = 1 × 17 + 13
  2. 17 = 1 × 13 + 4
  3. 13 = 3 × 4 + 1
  4. 4 = 4 × 1 + 0

The last non-zero remainder is 1, so GCF(17, 30) = 1.

LCM by listing multiples

Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, ...
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, ...
The first number in both lists is 510.

Check: GCF × LCM = product

1 × 510 = 510 = 17 × 30. This always holds for two numbers, so you can find the LCM as (17 × 30) ÷ 1 = 510.

Simplifying the fraction 17/30

17/30 is already in lowest terms because the GCF of 17 and 30 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 17134
3 and 17151
4 and 17168
5 and 17185
6 and 171102
7 and 171119
2 and 30230
3 and 30330
4 and 30260
5 and 30530
6 and 30630
7 and 301210

See also: factors of 17 · factors of 30.

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