+2653 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?
+1926 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! :)
+129895 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
+1926 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
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