SOLUTION: What is the smallest positive integer divisible by all of the first ten positive integers?

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Question 246694: What is the smallest positive integer divisible by all of the first ten positive integers?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Another way to word this problem is: "Find the least common multiple (LCM) of the first ten positive integers."

One way to find 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
The LCM of all of these will be the product of all the different factors. When a factor appears in more than one list of factors, use the longest string of this factor. So:
LCM = 1*2*2*2*3*3*5*7 = 2520
(The factors 2 and 3 appeared in more than one list of factors. So we use the longest string of each. We used the string of 3 2's from the list of factors for 8 and the string of 2 3's from the list of factors for 9.)