LCM of 8 and 12
The least common multiple of 8 and 12 is 24 — the smallest positive number into which both 8 and 12 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 24.
8 and 12 share the factor 4, so their first meeting point comes earlier than the raw product: the LCM is (8 × 12) ÷ 4 = 96 ÷ 4 = 24. Both numbers divide it exactly — 8 fits 3 times and 12 fits 2 times — and the pairing identity LCM × GCF = a × b holds again: 24 × 4 = 96. After 24, the lines re-synchronize for good, so the common multiples continue 48, 72, 96, and onward.
| # | Common multiple |
|---|---|
| 1 | 24 |
| 2 | 48 |
| 3 | 72 |
| 4 | 96 |
| 5 | 120 |
| 6 | 144 |
| 7 | 168 |
| 8 | 192 |
| 9 | 216 |
| 10 | 240 |
| 11 | 264 |
| 12 | 288 |
Frequently asked questions
What is the LCM of 8 and 12?
The least common multiple of 8 and 12 is 24. The multiples of 8 begin 8, 16, 24, 32, … and the multiples of 12 begin 12, 24, 36, …, and 24 is the first value both lists share. Formula check: (8 × 12) ÷ GCF(8, 12) = 96 ÷ 4 = 24.
How do you find the LCM of 8 and 12?
Compare prime factorizations: 8 = 2³ and 12 = 2² × 3. Carry every prime at its highest power into the answer: 2³ × 3 = 24. The shortcut through the GCF lands on the same value: (8 × 12) ÷ 4 = 24.
What is the GCF of 8 and 12?
4. The largest number dividing both. The identity GCF × LCM = 8 × 12 checks it against this page: 4 × 24 = 96. The same GCF reduces fractions built on 8 and 12, while 24 is the common denominator that needs no reducing.
What are the common multiples of 8 and 12?
Exactly the multiples of the LCM: 24, 48, 72, 96, 120, 144, and onward without end. The table above lists the first twelve; every later one is another 24 steps out. These are the numbers into which both 8 and 12 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.