Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

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

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

Relevance

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

----------------------------

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

• 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.

Source(s): Has been answered before. And well!
• 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

:)>

• 1=1

2=2

3=3

4=2*2

5=5

6=2*3

7=7

8=2*2*2

9=3*3

• Zero divided by any number is still zero.

• Find the L.C.M of 1,2,3,4,5,6,7,8,9

that is

2520

• Anonymous
9 years ago

lcm(1,2,3,4,5,6,7,8,9)=8*5*7*9

• Anonymous
9 years ago

3060