LCM for 12, 14 and 20
"Least Common Multiple of 3 Numbers" Calculator
What's the Least Common Multiple (LCM) of 12, 14 and 20?
Answer
LCM of 12, 14 and 20 is
420
First common multiples: 420; 840; 1,260; …
420 is divisible by all three: 420 ÷ 12 = 35, 420 ÷ 14 = 30, 420 ÷ 20 = 21 — and 35, 30 and 21 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/12 by 35 and of y/14 by 30 and of z/20 by 21.
12 = 22 × 3
14 = 2 × 7
20 = 22 × 5
| Prime | 12 | 14 | 20 | Highest power |
|---|---|---|---|---|
| 2 | 22 | 2 | 22 | 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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