LCM of 12 and 18
The least common multiple of 12 and 18 is 36 — the smallest positive number into which both 12 and 18 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 36.
12 and 18 share the factor 6, so their first meeting point comes earlier than the raw product: the LCM is (12 × 18) ÷ 6 = 216 ÷ 6 = 36. Both numbers divide it exactly — 12 fits 3 times and 18 fits 2 times — and the pairing identity LCM × GCF = a × b holds again: 36 × 6 = 216. 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 12 and 18?
The least common multiple of 12 and 18 is 36. The multiples of 12 begin 12, 24, 36, 48, … and the multiples of 18 begin 18, 36, 54, …, and 36 is the first value both lists share. Formula check: (12 × 18) ÷ GCF(12, 18) = 216 ÷ 6 = 36.
How do you find the LCM of 12 and 18?
Compare prime factorizations: 12 = 2² × 3 and 18 = 2 × 3². Carry every prime at its highest power into the answer: 2² × 3² = 36. The shortcut through the GCF lands on the same value: (12 × 18) ÷ 6 = 36.
What is the GCF of 12 and 18?
6. The largest number dividing both. The identity GCF × LCM = 12 × 18 checks it against this page: 6 × 36 = 216. The same GCF reduces fractions built on 12 and 18, while 36 is the common denominator that needs no reducing.
What are the common multiples of 12 and 18?
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 12 and 18 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.