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Amos counts out loud by six beginning with $0.$ Sarah counts out loud by three also beginning with $0.$ Between $0$ and $100$ inclusive, how many of the numbers do both Sarah and Amos say out loud?

 Jun 3, 2024
 #1
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Well, notice that LCM[6, 3], is 6, so every factor of 6 between 0 and 100 is a factor. 

 

We have \(100/6=16.67\), rounding down means there are 16 factors. 

 

However, this is not including 0, so we add 1 to get 17. 

 

So both Sarah and Amos say 17 numbers out loud. 

 

Thanks! :)

 Jun 3, 2024

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