Question 505530: Find the smallest number evenly divisible by each counting number from 1 to 10. Explain in detail explanation.
Answer by Edwin McCravy(20065)   (Show Source):
You can put this solution on YOUR website! 2520
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 facor each of 5 and 7
LCM = 2*2*2*3*3*5*7 = 2520
Edwin
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