LCM of 3 and 12
The least common multiple of 3 and 12 is 12 — the smallest positive number into which both 3 and 12 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 12.
12 is already a multiple of 3 — 3 divides it exactly (3 × 4 = 12) — so the smaller number never needs to climb past it: the LCM is 12 itself, and every multiple of 12 is automatically a common multiple. The two skip-count lines meet at once and re-meet every 12 steps: 12, 24, 36, and onward. This is why the LCM collapses to the larger number whenever the smaller divides the larger; the GCF here is 3, and the pairing identity LCM × GCF = a × b confirms it: 12 × 3 = 36.
| # | Common multiple |
|---|---|
| 1 | 12 |
| 2 | 24 |
| 3 | 36 |
| 4 | 48 |
| 5 | 60 |
| 6 | 72 |
| 7 | 84 |
| 8 | 96 |
| 9 | 108 |
| 10 | 120 |
| 11 | 132 |
| 12 | 144 |
Frequently asked questions
What is the LCM of 3 and 12?
12. Since 12 is already a multiple of 3 (3 × 4 = 12), the two multiple lists meet right there — 12 is the first number both divide evenly. The formula agrees: (3 × 12) ÷ GCF(3, 12) = 36 ÷ 3 = 12.
How do you find the LCM of 3 and 12?
Check divisibility first: when the smaller number divides the larger, the larger number is the LCM. Here 3 divides 12 (3 × 4 = 12), so nothing else is needed. Prime factorizations confirm it: 3 = 3 and 12 = 2² × 3, and carrying every prime at its highest power gives 2² × 3 = 12.
What is the GCF of 3 and 12?
3. The largest number dividing both. The identity GCF × LCM = 3 × 12 checks it against this page: 3 × 12 = 36. The same GCF reduces fractions built on 3 and 12, while 12 is the common denominator that needs no reducing.
What are the common multiples of 3 and 12?
Exactly the multiples of the LCM: 12, 24, 36, 48, 60, 72, and onward without end. The table above lists the first twelve; every later one is another 12 steps out. These are the numbers into which both 3 and 12 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.