Intermath | Workshop Support
 Write-up 5

Title
Dividing Primes

Problem Statement
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.

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 .

Author & Contact
Teresa Johnson
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