<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-three-ringing-bells">Three Ringing Bells Exercise</a></span></p><p>You might come across a word problem with a scenario that we call the <strong><span style="color:#27ae60;">Three Ringing Bells</span></strong> problem. In these problems, you're presented with three or four numbers that occur in regular intervals. The problem usually states that all of these instances occur at the same time at some point. They then ask you how much time will elapse before they all occur simultaneously again. To solve these problems, simply find the Least Common Multiple of the three or four numbers.</p>
<p><strong><span style="color:#e74c3c;"><span style="font-size:20px;">Example</span></span></strong></p>
<p>In an industrial kitchen, a cake is completed every $10$ minutes, a tray of brownies every $12$ minutes, and a tray of sugar cookies every $8$ minutes. If at noon, a cake, tray of brownies, and tray of sugar cookies are completed at the same time, how many minutes will elapse before all three are completed at the same time again?</p>
<p>To solve, simply find the LCM of $10 \ (2^15^1)$, $12 \ (2^23^1)$, and $8 \ (2^3)$.</p>
<p>$$2^33^15^1 = 120$$</p>
<p>So $120$ minutes will elapse before they all come out at the same time again.</p>