LCM of 30 and 45
The least common multiple of 30 and 45 is 90 — the smallest positive number into which both 30 and 45 divide evenly. This page lists the first twelve common multiples of the pair, which are exactly the multiples of 90.
30 and 45 share the factor 15, so their first meeting point comes earlier than the raw product: the LCM is (30 × 45) ÷ 15 = 1350 ÷ 15 = 90. Both numbers divide it exactly — 30 fits 3 times and 45 fits 2 times — and the pairing identity LCM × GCF = a × b holds again: 90 × 15 = 1350. After 90, the lines re-synchronize for good, so the common multiples continue 180, 270, 360, and onward.
| # | Common multiple |
|---|---|
| 1 | 90 |
| 2 | 180 |
| 3 | 270 |
| 4 | 360 |
| 5 | 450 |
| 6 | 540 |
| 7 | 630 |
| 8 | 720 |
| 9 | 810 |
| 10 | 900 |
| 11 | 990 |
| 12 | 1080 |
Frequently asked questions
What is the LCM of 30 and 45?
The least common multiple of 30 and 45 is 90. The multiples of 30 begin 30, 60, 90, 120, … and the multiples of 45 begin 45, 90, 135, …, and 90 is the first value both lists share. Formula check: (30 × 45) ÷ GCF(30, 45) = 1350 ÷ 15 = 90.
How do you find the LCM of 30 and 45?
Compare prime factorizations: 30 = 2 × 3 × 5 and 45 = 3² × 5. Carry every prime at its highest power into the answer: 2 × 3² × 5 = 90. The shortcut through the GCF lands on the same value: (30 × 45) ÷ 15 = 90.
What is the GCF of 30 and 45?
15. The largest number dividing both. The identity GCF × LCM = 30 × 45 checks it against this page: 15 × 90 = 1350. The same GCF reduces fractions built on 30 and 45, while 90 is the common denominator that needs no reducing.
What are the common multiples of 30 and 45?
Exactly the multiples of the LCM: 90, 180, 270, 360, 450, 540, and onward without end. The table above lists the first twelve; every later one is another 90 steps out. These are the numbers into which both 30 and 45 divide evenly — which is why the LCM itself is the natural common denominator in fraction work.