LCM for 7, 8 and 12
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What's the Least Common Multiple (LCM) of 7, 8 and 12?
Answer
LCM of 7, 8 and 12 is
168
First common multiples: 168, 336, 504, …
168 is divisible by all three: 168 ÷ 7 = 24, 168 ÷ 8 = 21, 168 ÷ 12 = 14 — and 24, 21 and 14 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/7 by 24 and of y/8 by 21 and of z/12 by 14.
7 — prime
8 = 23
12 = 22 × 3
| Prime | 7 | 8 | 12 | Highest power |
|---|---|---|---|---|
| 2 | — | 23 | 22 | 23 |
| 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 = 23 × 3 × 7 = 168
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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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