LCM for 5, 10 and 12
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What's the Least Common Multiple (LCM) of 5, 10 and 12?
Answer
LCM of 5, 10 and 12 is
60
First common multiples: 60, 120, 180, …
60 is divisible by all three: 60 ÷ 5 = 12, 60 ÷ 10 = 6, 60 ÷ 12 = 5 — and 12, 6 and 5 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/5 by 12 and of y/10 by 6 and of z/12 by 5.
5 — prime
10 = 2 × 5
12 = 22 × 3
| Prime | 5 | 10 | 12 | Highest power |
|---|---|---|---|---|
| 2 | — | 2 | 22 | 22 |
| 3 | — | — | 3 | 3 |
| 5 | 5 | 5 | — | 5 |
— = 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 = 60
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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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