LCM for 10, 12 and 14
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What's the Least Common Multiple (LCM) of 10, 12 and 14?
Answer
LCM of 10, 12 and 14 is
420
First common multiples: 420; 840; 1,260; …
420 is divisible by all three: 420 ÷ 10 = 42, 420 ÷ 12 = 35, 420 ÷ 14 = 30 — and 42, 35 and 30 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/10 by 42 and of y/12 by 35 and of z/14 by 30.
10 = 2 × 5
12 = 22 × 3
14 = 2 × 7
| Prime | 10 | 12 | 14 | Highest power |
|---|---|---|---|---|
| 2 | 2 | 22 | 2 | 22 |
| 3 | — | 3 | — | 3 |
| 5 | 5 | — | — | 5 |
| 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 × 5 × 7 = 420
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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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