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Divides them all.... (Posted on 2010-11-11) Difficulty: 2 of 5
What is the smallest positive number that is evenly divisible by each of the integers from 1 to 24 -inclusive?

No Solution Yet Submitted by Ady TZIDON    
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Solution EASY solution Comment 2 of 2 |
The solution to this question is rather very simple.
The number which the question require si the LCM of 1,2,3......23,24
which is equal to 2^4*3^2*5*7*11*13*17*19*23= 5354228880.

How to find the LCM:
1=1                                       2=2
3=3                                       4=2^2
5=5                                       6=2*3
7=7                                       8=2^3
9=3^2                                   10=2*5
11=11                                    12=2^2*3
13=13                                    14=2*7
15=3*5                                  16=2^4
17=17                                    18=2*3^2
19=19                                    20=2^2*5
21=3*7                                  22=2*11
23=23                                    24=2^3*3

Therefore the LCM =the highest power of 2,3,5,7,11,13,17,19,23
                         = 2^4*3^2*5*7*11*13*17*19*23
                         = 5354228880.


  Posted by Danish Ahmed Khan on 2012-10-27 07:07:41
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