LCM for 12, 18 and 20
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What's the Least Common Multiple (LCM) of 12, 18 and 20?
Answer
LCM of 12, 18 and 20 is
180
First common multiples: 180, 360, 540, …
180 is divisible by all three: 180 ÷ 12 = 15, 180 ÷ 18 = 10, 180 ÷ 20 = 9 — and 15, 10 and 9 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/12 by 15 and of y/18 by 10 and of z/20 by 9.
12 = 22 × 3
18 = 2 × 32
20 = 22 × 5
| Prime | 12 | 18 | 20 | Highest power |
|---|---|---|---|---|
| 2 | 22 | 2 | 22 | 22 |
| 3 | 3 | 32 | — | 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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