LCM for 3, 9 and 12
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What's the Least Common Multiple (LCM) of 3, 9 and 12?
Answer
LCM of 3, 9 and 12 is
36
First common multiples: 36, 72, 108, …
36 is divisible by all three: 36 ÷ 3 = 12, 36 ÷ 9 = 4, 36 ÷ 12 = 3 — and 12, 4 and 3 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 12 and of y/9 by 4 and of z/12 by 3.
3 — prime
9 = 32
12 = 22 × 3
| Prime | 3 | 9 | 12 | Highest power |
|---|---|---|---|---|
| 2 | — | — | 22 | 22 |
| 3 | 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 = 22 × 32 = 36
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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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