LCM of 9 and 15
The least common multiple of 9 and 15 is 45 — the smallest positive number into which both 9 and 15 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 45.
9 and 15 share the factor 3, so their first meeting point comes earlier than the raw product: the LCM is (9 × 15) ÷ 3 = 135 ÷ 3 = 45. Both numbers divide it exactly — 9 fits 5 times and 15 fits 3 times — and the pairing identity LCM × GCF = a × b holds again: 45 × 3 = 135. After 45, the lines re-synchronize for good, so the common multiples continue 90, 135, 180, and onward.
| # | Common multiple |
|---|---|
| 1 | 45 |
| 2 | 90 |
| 3 | 135 |
| 4 | 180 |
| 5 | 225 |
| 6 | 270 |
| 7 | 315 |
| 8 | 360 |
| 9 | 405 |
| 10 | 450 |
| 11 | 495 |
| 12 | 540 |
Frequently asked questions
What is the LCM of 9 and 15?
The least common multiple of 9 and 15 is 45. The multiples of 9 begin 9, 18, 27, 36, … and the multiples of 15 begin 15, 30, 45, …, and 45 is the first value both lists share. Formula check: (9 × 15) ÷ GCF(9, 15) = 135 ÷ 3 = 45.
How do you find the LCM of 9 and 15?
Compare prime factorizations: 9 = 3² and 15 = 3 × 5. Carry every prime at its highest power into the answer: 3² × 5 = 45. The shortcut through the GCF lands on the same value: (9 × 15) ÷ 3 = 45.
What is the GCF of 9 and 15?
3. The largest number dividing both. The identity GCF × LCM = 9 × 15 checks it against this page: 3 × 45 = 135. The same GCF reduces fractions built on 9 and 15, while 45 is the common denominator that needs no reducing.
What are the common multiples of 9 and 15?
Exactly the multiples of the LCM: 45, 90, 135, 180, 225, 270, and onward without end. The table above lists the first twelve; every later one is another 45 steps out. These are the numbers into which both 9 and 15 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.