LCM for 8, 9 and 12
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What's the Least Common Multiple (LCM) of 8, 9 and 12?
Answer
LCM of 8, 9 and 12 is
72
First common multiples: 72, 144, 216, …
72 is divisible by all three: 72 ÷ 8 = 9, 72 ÷ 9 = 8, 72 ÷ 12 = 6 — and 9, 8 and 6 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/8 by 9 and of y/9 by 8 and of z/12 by 6.
8 = 23
9 = 32
12 = 22 × 3
| Prime | 8 | 9 | 12 | Highest power |
|---|---|---|---|---|
| 2 | 23 | — | 22 | 23 |
| 3 | — | 32 | 3 | 32 |
— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.
LCM = 23 × 32 = 72
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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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