GCF and LCM of 18 and 48
GCF 6 · LCM 144
The greatest common divisor (GCD) and the highest common factor (HCF) are the same number as the GCF above — three names for the largest number that divides both 18 and 48 without a remainder. The least common multiple is sometimes written LCM or lowest common multiple.
Checked by test against every pair in this family · How we check
The Euclidean algorithm, step by step
Divide the larger by the smaller, keep the remainder, repeat with the last two numbers. When the remainder reaches zero, the number you last divided by is the answer.
- 48 ÷ 18 leaves 12
- 18 ÷ 12 leaves 6
- 12 ÷ 6 leaves 0 — so the GCF is 6
The same answer from the prime factors
- 18 factors as
- 2 × 3²
- 48 factors as
- 2⁴ × 3
- Shared, at the lower power of each
- 2 × 3
Multiply the shared primes and you get 6, the same number the division produced. The LCM takes the higher power of every prime in either list instead, which gives 144.
The check that makes it certain
6 × 144 = 864 = 18 × 48
For any two whole numbers the greatest common factor and the least common multiple multiply to the numbers themselves. Everything one of them leaves out, the other takes in. It also means you never need to compute both: divide the product by the one you have.
What each one is actually for
The greatest common factor reduces a fraction. 18/48 ÷ 6 = 3/8, and no smaller pair of whole numbers gives the same value.
The least common multiple is the denominator two fractions have to share before they can be added. 1/18 + 1/48 = 8/144 + 3/144 = 11/144. Any common multiple would work; this is the smallest, so the numbers stay as small as they can.
Those are the two jobs. Everything else on this page is how to find them. Reduce any fraction or add two of them.