Question

which is the smallest number divisible by 1 2 3 4 5 6 7 8 and 9 ?​

Answer 1

Answer:

1

Expansion

1

Lcm of 1, 2,3,4,5,6,7,8,9 is 1

Answer 2

Answer:

2520

Step-by-step explanation:

We want LCM(1,2,3,4,5,6,7,8,9,10)

We can ignore 1, since any counting number is divisible by 1.

We prime factor each of the counting numbers from 2 to 10

2 = 2

3 = 3

4 = 2*2

5 = 5

6 = 2*3

7 = 7

8 = 2*2*2

9 = 3*3

10 = 2*5

The LCM of all those must have as many factors of

each prime that appears in any factorization

2 appears at most 3 times as a factor of 8

3 appears at most 2 times as a factor of 9

5 appears at most 1 time as a factor if 5 and 10

7 appears at most 1 time as a factor of 7

So the LCM has

3 factors of 2, 2 factors of 3, and 1 factor each of 5 and 7

LCM = 2*2*2*3*3*5*7 = 2520