What is the smallest positive integer that is divisible by all the integers from 1 to 16?

Question

It's all inclusive between 1 and 16

Answer 1

First find the least common multiple (LCM) of all the integers 1 to 16. One way to find the LCM's is to use prime factorization. 

 

1 = 1

2 = 2

3 = 3

4 = 2 * 2 

5 = 5

6 = 2 * 3

7 = 7

8 = 2 * 2 * 2

9 = 3 * 3

10 = 2 * 5

11 = 11

12 = 2 * 2 * 3

13 = 13

14 = 2 * 7

15 = 3 * 5

16 = 2 * 2 * 2 * 2

 

The LCM of all these will be the product of all the different factors. When a factor appears more than once in list of factors, use the the longest string of this factor. So, LCM = 1*2*2*2*2*3*3*5*7*11*13 = 720720.