LCM for 30 and 105
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What's the Least Common Multiple (LCM) of 30 and 105?
Answer
LCM of 30 and 105 is
210
First common multiples: 210, 420, 630, …
210 is divisible by both: 210 ÷ 30 = 7, 210 ÷ 105 = 2 — and 7 and 2 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/30 by 7 and of y/105 by 2.
30 = 2 × 3 × 5
105 = 3 × 5 × 7
| Prime | 30 | 105 | Highest power |
|---|---|---|---|
| 2 | 2 | — | 2 |
| 3 | 3 | 3 | 3 |
| 5 | 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 - Find the Greatest Common Factor (GCF) of two numbers
- Least Common Multiple of 3 Numbers - Find the Least Common Multiple (LCM) of three numbers
- Greatest Common Factor of 3 Numbers - Find the Greatest Common Factor (GCF) of three numbers
- Multiples of a Number - List the first 10 multiples of any number from 1 to 999
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