LCM of 9 and 12
The least common multiple of 9 and 12 is 36 — the smallest positive number into which both 9 and 12 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 36.
9 and 12 share the factor 3, so their first meeting point comes earlier than the raw product: the LCM is (9 × 12) ÷ 3 = 108 ÷ 3 = 36. Both numbers divide it exactly — 9 fits 4 times and 12 fits 3 times — and the pairing identity LCM × GCF = a × b holds again: 36 × 3 = 108. After 36, the lines re-synchronize for good, so the common multiples continue 72, 108, 144, and onward.
| # | Common multiple |
|---|---|
| 1 | 36 |
| 2 | 72 |
| 3 | 108 |
| 4 | 144 |
| 5 | 180 |
| 6 | 216 |
| 7 | 252 |
| 8 | 288 |
| 9 | 324 |
| 10 | 360 |
| 11 | 396 |
| 12 | 432 |
Frequently asked questions
What is the LCM of 9 and 12?
The least common multiple of 9 and 12 is 36. The multiples of 9 begin 9, 18, 27, 36, … and the multiples of 12 begin 12, 24, 36, …, and 36 is the first value both lists share. Formula check: (9 × 12) ÷ GCF(9, 12) = 108 ÷ 3 = 36.
How do you find the LCM of 9 and 12?
Compare prime factorizations: 9 = 3² and 12 = 2² × 3. Carry every prime at its highest power into the answer: 2² × 3² = 36. The shortcut through the GCF lands on the same value: (9 × 12) ÷ 3 = 36.
What is the GCF of 9 and 12?
3. The largest number dividing both. The identity GCF × LCM = 9 × 12 checks it against this page: 3 × 36 = 108. The same GCF reduces fractions built on 9 and 12, while 36 is the common denominator that needs no reducing.
What are the common multiples of 9 and 12?
Exactly the multiples of the LCM: 36, 72, 108, 144, 180, 216, and onward without end. The table above lists the first twelve; every later one is another 36 steps out. These are the numbers into which both 9 and 12 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.