LCM of 12 and 16
The least common multiple of 12 and 16 is 48 — the smallest positive number into which both 12 and 16 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 48.
12 and 16 share the factor 4, so their first meeting point comes earlier than the raw product: the LCM is (12 × 16) ÷ 4 = 192 ÷ 4 = 48. Both numbers divide it exactly — 12 fits 4 times and 16 fits 3 times — and the pairing identity LCM × GCF = a × b holds again: 48 × 4 = 192. After 48, the lines re-synchronize for good, so the common multiples continue 96, 144, 192, and onward.
| # | Common multiple |
|---|---|
| 1 | 48 |
| 2 | 96 |
| 3 | 144 |
| 4 | 192 |
| 5 | 240 |
| 6 | 288 |
| 7 | 336 |
| 8 | 384 |
| 9 | 432 |
| 10 | 480 |
| 11 | 528 |
| 12 | 576 |
Frequently asked questions
What is the LCM of 12 and 16?
The least common multiple of 12 and 16 is 48. The multiples of 12 begin 12, 24, 36, 48, … and the multiples of 16 begin 16, 32, 48, …, and 48 is the first value both lists share. Formula check: (12 × 16) ÷ GCF(12, 16) = 192 ÷ 4 = 48.
How do you find the LCM of 12 and 16?
Compare prime factorizations: 12 = 2² × 3 and 16 = 2⁴. Carry every prime at its highest power into the answer: 2⁴ × 3 = 48. The shortcut through the GCF lands on the same value: (12 × 16) ÷ 4 = 48.
What is the GCF of 12 and 16?
4. The largest number dividing both. The identity GCF × LCM = 12 × 16 checks it against this page: 4 × 48 = 192. The same GCF reduces fractions built on 12 and 16, while 48 is the common denominator that needs no reducing.
What are the common multiples of 12 and 16?
Exactly the multiples of the LCM: 48, 96, 144, 192, 240, 288, and onward without end. The table above lists the first twelve; every later one is another 48 steps out. These are the numbers into which both 12 and 16 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.