SOLUTION: 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

Question 1207612: 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?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i must admit i struggled with this, but i found a calculator on the web that told me different ways to find the answer in addition to find the answer for me.

that calculator can be found at https://www.calculatorsoup.com/calculators/math/lcm.php

the answer is 4140.
that's the least common multiple.

the calculator gives you the answer PLUS it describes how the answer was derived, using different methods.

for example, i selected GCF method (greatest common factor).

it solved the problem by doing the following:

you are looking for the least common multiple for 36, 90, 345.

first find the greatest common factor for 36, 90.
that turns out to be 18, because 18 is the greatest common factor that divides evenly into 36 and 90.
36 * 90 / 18 = 180.

you now want to find the greatest common factor of 180, 345.
that turns out to be 15, because 15 is the greatest common factor that divides evenly into 180 and 345.
180 * 345 / 15 = 4140.

your least common multiplier is 4140.

try the calculator out for yourself and go through the different methods.
it provides the answer and instructs you on how the answer was derived.

very neat.

Answer by ikleyn(52817) (Show Source): You can put this solution on YOUR website!
.

They want you find the Less Common Multiple of numbers 36, 90 and 385 seconds, and then convert this numbers from seconds to minutes. 36 = 2^2*3^2; 90 = 2*3^2*5; 385 = 5*7*11. To find LCM, we take the prime factor from each decomposition with the highest possible index. Thus we get LCM(36, 90, 385) = 2^2*3^2*5*7*11 = 13860 seconds. We convert it from seconds to minutes by dividing by 60. Doing this way, we get the ANSWER. 231 minutes.

Solved, with complete explanations attached.

==================

The solution by @Theo is irrelevant, since he mistakenly used the value of
345 seconds instead of the given value of 385 seconds.

Thus his answer is INCORRECT.

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