LCM for 8, 12 and 30
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What's the Least Common Multiple (LCM) of 8, 12 and 30?
Answer
LCM of 8, 12 and 30 is
120
First common multiples: 120, 240, 360, …
120 is divisible by all three: 120 ÷ 8 = 15, 120 ÷ 12 = 10, 120 ÷ 30 = 4 — and 15, 10 and 4 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 15 and of y/12 by 10 and of z/30 by 4.
8 = 23
12 = 22 × 3
30 = 2 × 3 × 5
| Prime | 8 | 12 | 30 | Highest power |
|---|---|---|---|---|
| 2 | 23 | 22 | 2 | 23 |
| 3 | — | 3 | 3 | 3 |
| 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 = 23 × 3 × 5 = 120
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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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