Quandaries
and Queries |
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Name: Simon Who is asking: Student Level of the question: Secondary Question: determine smallest positive integer that is divisible by each of the first ten counting numbers |
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Hi Simon, I'm going to find the smallest positive integer N that is divisible by each of the first The first step is to find the prime decompositions.
The primes that appear in these decompositions are 2, 3 and 5. Since each of these counting numbers divide N, the three primes 2, 3 and 5 must divide N. Since these are the only primes that divide these counting numbers and since I want N to be as small as possible, the only primes that divide N are 2, 3 and 5. Thus the prime factorization of N is
All that is left is to determine what valued go in for the question marks. I want these values to be as small as possible to keep N small. 5 only appears once in the factorizations above (5 = 5
3 appears twice in the factorizations, (3 = 3
Finally, 2 appears 3 times and in one of these (4 = 2
Now you try the first ten counting numbers. Penny |