LCM for 6, 7 and 10
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What's the Least Common Multiple (LCM) of 6, 7 and 10?
Answer
LCM of 6, 7 and 10 is
210
First common multiples: 210, 420, 630, …
210 is divisible by all three: 210 ÷ 6 = 35, 210 ÷ 7 = 30, 210 ÷ 10 = 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/6 by 35 and of y/7 by 30 and of z/10 by 21.
6 = 2 × 3
7 — prime
10 = 2 × 5
| Prime | 6 | 7 | 10 | Highest power |
|---|---|---|---|---|
| 2 | 2 | — | 2 | 2 |
| 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 = 2 × 3 × 5 × 7 = 210
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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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