LCM for 3, 12 and 30
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What's the Least Common Multiple (LCM) of 3, 12 and 30?
Answer
LCM of 3, 12 and 30 is
60
First common multiples: 60, 120, 180, …
60 is divisible by all three: 60 ÷ 3 = 20, 60 ÷ 12 = 5, 60 ÷ 30 = 2 — and 20, 5 and 2 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/3 by 20 and of y/12 by 5 and of z/30 by 2.
3 — prime
12 = 22 × 3
30 = 2 × 3 × 5
| Prime | 3 | 12 | 30 | Highest power |
|---|---|---|---|---|
| 2 | — | 22 | 2 | 22 |
| 3 | 3 | 3 | 3 | 3 |
| 5 | — | — | 5 | 5 |
— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.
LCM = 22 × 3 × 5 = 60
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See Also
- Greatest Common Factor of 3 Numbers - Find the Greatest Common Factor (GCF) of three numbers
- Least Common Multiple - Find the Least Common Multiple (LCM) of two numbers
- Greatest Common Factor - Find the Greatest Common Factor (GCF) of two numbers
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LCM Table
| 1st | 2nd | 3rd | LCM |
|---|---|---|---|
| 3 | 12 | 15 | 60 |
| 3 | 12 | 16 | 48 |
| 3 | 12 | 17 | 204 |
| 3 | 12 | 18 | 36 |
| 3 | 12 | 19 | 228 |
| 3 | 12 | 20 | 60 |
| 3 | 12 | 21 | 84 |
| 3 | 12 | 22 | 132 |
| 3 | 12 | 23 | 276 |
| 3 | 12 | 24 | 24 |
| 3 | 12 | 25 | 300 |
| 3 | 12 | 26 | 156 |
| 3 | 12 | 27 | 108 |
| 3 | 12 | 28 | 84 |
| 3 | 12 | 29 | 348 |
| 3 | 12 | 30 | 60 |
| 3 | 12 | 31 | 372 |
| 3 | 12 | 32 | 96 |
| 3 | 12 | 33 | 132 |
| 3 | 12 | 34 | 204 |
| 3 | 12 | 35 | 420 |
| 3 | 12 | 36 | 36 |
| 3 | 12 | 37 | 444 |
| 3 | 12 | 38 | 228 |
| 3 | 12 | 39 | 156 |
| 3 | 12 | 40 | 120 |
| 3 | 12 | 41 | 492 |
| 3 | 12 | 42 | 84 |
| 3 | 12 | 43 | 516 |
| 3 | 12 | 44 | 132 |