LCM for 6, 7 and 12
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What's the Least Common Multiple (LCM) of 6, 7 and 12?
Answer
LCM of 6, 7 and 12 is
84
First common multiples: 84, 168, 252, …
84 is divisible by all three: 84 ÷ 6 = 14, 84 ÷ 7 = 12, 84 ÷ 12 = 7 — and 14, 12 and 7 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/6 by 14 and of y/7 by 12 and of z/12 by 7.
6 = 2 × 3
7 — prime
12 = 22 × 3
| Prime | 6 | 7 | 12 | Highest power |
|---|---|---|---|---|
| 2 | 2 | — | 22 | 22 |
| 3 | 3 | — | 3 | 3 |
| 7 | — | 7 | — | 7 |
— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.
LCM = 22 × 3 × 7 = 84
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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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