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# What is the smallest number that is....?

Exactly divisible by 1,2,3,4,5,6,7,8 and9?

### 8 Answers

- Iggy RockoLv 79 years agoFavorite Answer
1: 1

2: 1*2

3: 1*........3

4: 1*2*2

5: 1*..............5

6: 1*2*.....3

7: 1*.................7

8: 1*2*2*2

9: 1*........3*3

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....1*2*2*2*3*3*5*7 = 2520 = LCM of 1, 2, 3, 4, 5, 6, 7, 8, and 9

- 9 years ago
Best way:

"Compute the prime factors of each of the factors:

1 = 1

2 = 2

3 = 3

4 = 2*2

5 = 5

6 = 2*3

7 = 7

8 = 2*2*2

9 = 3*3

To get our least common multiple, combine the highest powers of all the primes. For the 2's, that is 2*2*2. For the 3's, that would be 3*3. We also have one each of a 5 and a 7. The least common multiple is the product of all these, which is 2*2*2*3*3*5*7 = 2520. By the way, you also get the factor 10 thrown in for free.

Answer by devilsadvocate1728 4 years ago."

Source(s): Has been answered before. And well! - Wayne DeguManLv 79 years ago
We require the lowest common multiple of these numbers. So, if we list the prime factors we get:

1-->1

2-->2

3-->3

4-->2²

5-->5

6-->2 x 3

7-->7

8-->2³

9-->3²

We now require the highest occuring power of each factor.

=> 2³ x 3² x 5 x 7

i.e. 8 x 9 x 5 x 7

so, 72 x 35 = 2,520

:)>

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- Anonymous9 years ago
lcm(1,2,3,4,5,6,7,8,9)=8*5*7*9

- Anonymous9 years ago
3060