LCM for 9, 12 and 15
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What's the Least Common Multiple (LCM) of 9, 12 and 15?
Answer
LCM of 9, 12 and 15 is
180
First common multiples: 180, 360, 540, …
180 is divisible by all three: 180 ÷ 9 = 20, 180 ÷ 12 = 15, 180 ÷ 15 = 12 — and 20, 15 and 12 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/9 by 20 and of y/12 by 15 and of z/15 by 12.
9 = 32
12 = 22 × 3
15 = 3 × 5
| Prime | 9 | 12 | 15 | Highest power |
|---|---|---|---|---|
| 2 | — | 22 | — | 22 |
| 3 | 32 | 3 | 3 | 32 |
| 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 × 32 × 5 = 180
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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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