LCM of 3 and 5
The least common multiple of 3 and 5 is 15 — the smallest positive number into which both 3 and 5 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 15.
3 and 5 share no common factor greater than 1, so their multiples first coincide only after a full 3 × 5 sweep: the LCM is the plain product 15. The number lines advance out of step — 3 every 3, 5 every 5 — and nothing shortens the wait. Because GCF(3, 5) = 1, the identity LCM × GCF = a × b reads 15 × 1 = 15, and the common multiples march outward at 15, 30, 45, and beyond.
| # | Common multiple |
|---|---|
| 1 | 15 |
| 2 | 30 |
| 3 | 45 |
| 4 | 60 |
| 5 | 75 |
| 6 | 90 |
| 7 | 105 |
| 8 | 120 |
| 9 | 135 |
| 10 | 150 |
| 11 | 165 |
| 12 | 180 |
Frequently asked questions
What is the LCM of 3 and 5?
The least common multiple of 3 and 5 is 15. The multiples of 3 begin 3, 6, 9, 12, … and the multiples of 5 begin 5, 10, 15, …, and 15 is the first value both lists share. Formula check: (3 × 5) ÷ GCF(3, 5) = 15 ÷ 1 = 15.
How do you find the LCM of 3 and 5?
Compare prime factorizations: 3 = 3 and 5 = 5. No prime is shared, so every prime enters at full power and the product is the LCM: 15. The shortcut through the GCF lands on the same value: (3 × 5) ÷ 1 = 15.
What is the GCF of 3 and 5?
1. The factorizations 3 and 5 share no prime, so 1 is the greatest common factor. The companion identity holds anyway: GCF × LCM = 3 × 5, or 1 × 15 = 15.
What are the common multiples of 3 and 5?
Exactly the multiples of the LCM: 15, 30, 45, 60, 75, 90, and onward without end. The table above lists the first twelve; every later one is another 15 steps out. These are the numbers into which both 3 and 5 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.