GCF and LCM of 11 and 14
GCF 1 · LCM 154
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 11 and 14 without a remainder. The least common multiple is sometimes written LCM or lowest common multiple.
11 and 14 share no factor above 1, which makes them coprime. That is why their least common multiple is simply 11 × 14 = 154: with nothing shared, nothing cancels.
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.
- 14 ÷ 11 leaves 3
- 11 ÷ 3 leaves 2
- 3 ÷ 2 leaves 1
- 2 ÷ 1 leaves 0 — so the GCF is 1
The same answer from the prime factors
- 11 factors as
- 11
- 14 factors as
- 2 × 7
- Shared, at the lower power of each
- none
Nothing appears in both lists, so the shared product is empty and the GCF is 1. The LCM takes every prime from both: 154.
The check that makes it certain
1 × 154 = 154 = 11 × 14
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. 11/14 is already in lowest terms — dividing by a GCF of 1 changes nothing, which is what coprime means in practice.
The least common multiple is the denominator two fractions have to share before they can be added. 1/11 + 1/14 = 14/154 + 11/154 = 25/154. 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.