How many of the first 100 positive whole numbers are divisible by all
three of the smallest prime numbers?
Plans to Solve/Investigate the Problem
My plan is to use an Excel spreadsheet to
display the solutions.
Investigation/Exploration of the Problem
First I identified the first 100 positive
whole numbers, that was easy, 1-100. Then I identified the
three smallest prime numbers, 2, 3, 5. Using an Excel spreadsheet
I numbered down one column 1-100. Then I used the next three
columns for my smallest prime numbers. I identified the numbers
that were divisible by 2 in yellow, 3 in red, and 5 in blue. To
determine which numbers met the original criteria I looked for the rows
that had all three columns highlighted.
Click here to
see Excel Spreadsheet
I found that there are three numbers in the
first 100 positive whole numbers that are divisible by all three of the
smallest prime numbers The solution set is: (30, 60, 90)
Other than being divisible by the smallest
three primes, 30, 60, and 90, 2 x 3 x 5 = 30 which is the least common
multiple of the three smallest primes, and 60 and 90 are multiples of 30
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