LCM of 6 and 9
The least common multiple of 6 and 9 is 18 — the smallest positive number into which both 6 and 9 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 18.
6 and 9 share the factor 3, so their first meeting point comes earlier than the raw product: the LCM is (6 × 9) ÷ 3 = 54 ÷ 3 = 18. Both numbers divide it exactly — 6 fits 3 times and 9 fits 2 times — and the pairing identity LCM × GCF = a × b holds again: 18 × 3 = 54. After 18, the lines re-synchronize for good, so the common multiples continue 36, 54, 72, and onward.
| # | Common multiple |
|---|---|
| 1 | 18 |
| 2 | 36 |
| 3 | 54 |
| 4 | 72 |
| 5 | 90 |
| 6 | 108 |
| 7 | 126 |
| 8 | 144 |
| 9 | 162 |
| 10 | 180 |
| 11 | 198 |
| 12 | 216 |
Frequently asked questions
What is the LCM of 6 and 9?
The least common multiple of 6 and 9 is 18. The multiples of 6 begin 6, 12, 18, 24, … and the multiples of 9 begin 9, 18, 27, …, and 18 is the first value both lists share. Formula check: (6 × 9) ÷ GCF(6, 9) = 54 ÷ 3 = 18.
How do you find the LCM of 6 and 9?
Compare prime factorizations: 6 = 2 × 3 and 9 = 3². Carry every prime at its highest power into the answer: 2 × 3² = 18. The shortcut through the GCF lands on the same value: (6 × 9) ÷ 3 = 18.
What is the GCF of 6 and 9?
3. The largest number dividing both. The identity GCF × LCM = 6 × 9 checks it against this page: 3 × 18 = 54. The same GCF reduces fractions built on 6 and 9, while 18 is the common denominator that needs no reducing.
What are the common multiples of 6 and 9?
Exactly the multiples of the LCM: 18, 36, 54, 72, 90, 108, and onward without end. The table above lists the first twelve; every later one is another 18 steps out. These are the numbers into which both 6 and 9 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.