LCM for 8, 15 and 21
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What's the Least Common Multiple (LCM) of 8, 15 and 21?
Answer
LCM of 8, 15 and 21 is
840
First common multiples: 840; 1,680; 2,520; …
840 is divisible by all three: 840 ÷ 8 = 105, 840 ÷ 15 = 56, 840 ÷ 21 = 40 — and 105, 56 and 40 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/8 by 105 and of y/15 by 56 and of z/21 by 40.
8 = 23
15 = 3 × 5
21 = 3 × 7
| Prime | 8 | 15 | 21 | Highest power |
|---|---|---|---|---|
| 2 | 23 | — | — | 23 |
| 3 | — | 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 = 23 × 3 × 5 × 7 = 840
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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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