GCF and LCM of 23 and 45

The GCF of 23 and 45 is 1. The LCM of 23 and 45 is 1,035.

• GCF (greatest common factor, also called GCD or HCF) of 23 and 45 = 1
• LCM (least common multiple) of 23 and 45 = 1,035

23 and 45 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 23 × 45 = 1,035.

Method 1: list the factors (GCF)

Factors of 23: 1, 23.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

23 = 23 (prime)
45 = 3 × 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: 3 × 3 × 5 × 23 = 1,035.

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. 45 = 1 × 23 + 22
2. 23 = 1 × 22 + 1
3. 22 = 22 × 1 + 0

The last non-zero remainder is 1, so GCF(23, 45) = 1.

LCM by listing multiples

Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, ...
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...
The first number in both lists is 1,035.

Check: GCF × LCM = product

1 × 1,035 = 1,035 = 23 × 45. This always holds for two numbers, so you can find the LCM as (23 × 45) ÷ 1 = 1,035.

Simplifying the fraction 23/45

23/45 is already in lowest terms because the GCF of 23 and 45 is 1.

GCF and LCM of similar pairs

See also: factors of 23 · factors of 45.

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