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Starting at the same time, Bill rings a bell every $36$ seconds, and Wendy blows a whistle every $90$ seconds, and Sam blows a horn every $385$ seconds.  How many minutes will it be before both Bill and Wendy and Sam simultaneously make a sound?

 Jun 20, 2024
 #1
avatar+1230 
+1

We want to find the LCM of 36, 90, and 385. 

We can use the cake and ladder method to complete this. We basically divide by prime numbers as long as two of the numbers are divisble by it. We write down the result and multiply the numbers in yellow. We get

 

Multyiplying the numbers in yellow, we get

\(2 * 3 * 3 * 5 * 2 * 77=13,860\)

 

So they ring the bell at 13,860 seconds. We want to convert into minutes. We get

\(13,860/60 = 231\)

 

So our answer is 231. 

 

Thanks! :)

 Jun 20, 2024
 #2
avatar+129725 
+1

That's an interesting method, NTS!!!!....I haven't seen that before....

 

Here's another way....factor each number

 

36  = 2^2 * 3^2

 

90  =  2 * 3^2 * 5

 

385  = 5 * 7 * 11

 

Take each different  prime to its  highest power and  find their product

 

2^2 * 3^2 * 5 * 7 * 11  = 13860 sec  =  231 min

 

cool cool cool

CPhill  Jun 20, 2024
 #3
avatar+1230 
+1

Cake and ladders is more for more basic levels. 

In my opinion, it gives awesome visual representations. 

It's inefficient for big numbers though...I would reccomend prime factorization for those numbers...

https://hootyshomeroom.com/simplifying-fractions-using-the-ladder-method/

 

Thanks! :)

 

~NTS

NotThatSmart  Jun 20, 2024
edited by NotThatSmart  Jun 21, 2024
 #4
avatar+22 
0

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 Jun 20, 2024
edited by derpmcfearson  Jun 20, 2024
 #5
avatar+129725 
0

Mmm...OK....

 

cool cool cool

CPhill  Jun 20, 2024

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