LCM of 6 and 10
The least common multiple of 6 and 10 is 30 — the smallest positive number into which both 6 and 10 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 30.
6 and 10 share the factor 2, so their first meeting point comes earlier than the raw product: the LCM is (6 × 10) ÷ 2 = 60 ÷ 2 = 30. Both numbers divide it exactly — 6 fits 5 times and 10 fits 3 times — and the pairing identity LCM × GCF = a × b holds again: 30 × 2 = 60. 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 6 and 10?
The least common multiple of 6 and 10 is 30. The multiples of 6 begin 6, 12, 18, 24, … and the multiples of 10 begin 10, 20, 30, …, and 30 is the first value both lists share. Formula check: (6 × 10) ÷ GCF(6, 10) = 60 ÷ 2 = 30.
How do you find the LCM of 6 and 10?
Compare prime factorizations: 6 = 2 × 3 and 10 = 2 × 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: (6 × 10) ÷ 2 = 30.
What is the GCF of 6 and 10?
2. The largest number dividing both. The identity GCF × LCM = 6 × 10 checks it against this page: 2 × 30 = 60. The same GCF reduces fractions built on 6 and 10, while 30 is the common denominator that needs no reducing.
What are the common multiples of 6 and 10?
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 6 and 10 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.