LCM of 10 and 15
The least common multiple of 10 and 15 is 30 — the smallest positive number into which both 10 and 15 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 30.
10 and 15 share the factor 5, so their first meeting point comes earlier than the raw product: the LCM is (10 × 15) ÷ 5 = 150 ÷ 5 = 30. Both numbers divide it exactly — 10 fits 3 times and 15 fits 2 times — and the pairing identity LCM × GCF = a × b holds again: 30 × 5 = 150. After 30, the lines re-synchronize for good, so the common multiples continue 60, 90, 120, and onward.
| # | Common multiple |
|---|---|
| 1 | 30 |
| 2 | 60 |
| 3 | 90 |
| 4 | 120 |
| 5 | 150 |
| 6 | 180 |
| 7 | 210 |
| 8 | 240 |
| 9 | 270 |
| 10 | 300 |
| 11 | 330 |
| 12 | 360 |
Frequently asked questions
What is the LCM of 10 and 15?
The least common multiple of 10 and 15 is 30. The multiples of 10 begin 10, 20, 30, 40, … and the multiples of 15 begin 15, 30, 45, …, and 30 is the first value both lists share. Formula check: (10 × 15) ÷ GCF(10, 15) = 150 ÷ 5 = 30.
How do you find the LCM of 10 and 15?
Compare prime factorizations: 10 = 2 × 5 and 15 = 3 × 5. Carry every prime at its highest power into the answer: 2 × 3 × 5 = 30. The shortcut through the GCF lands on the same value: (10 × 15) ÷ 5 = 30.
What is the GCF of 10 and 15?
5. The largest number dividing both. The identity GCF × LCM = 10 × 15 checks it against this page: 5 × 30 = 150. The same GCF reduces fractions built on 10 and 15, while 30 is the common denominator that needs no reducing.
What are the common multiples of 10 and 15?
Exactly the multiples of the LCM: 30, 60, 90, 120, 150, 180, and onward without end. The table above lists the first twelve; every later one is another 30 steps out. These are the numbers into which both 10 and 15 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.