TITLE: Please help me understand the solution of this question!
QUESTION [2 upvotes]: Question : Six bells commence tooling together and toll at intervals 2,4,6,8,10,12 minutes.In 30 hours,how many times do they toll together?
I found the LCM of 2,4,6,8,10,12 minutes in order to find the minimum minutes after they will tool together.
LCM (2,4,6,8,10,12)=120
It means they will toll together after 2 hours that is 120 mins.So in in 30 hours they should too together 15 times( 30/2).
But the answer provided in the textbook is 16 times.Can you please explain how they got 16?

REPLY [3 votes]: You have committed a fencepost (or Obi-wan) error. The question implies that the bells ring together at the very start of the $30$-hour period; $15$ periods of $120$ minutes pass, and then they ring together again at the very end of the $30$ hours. So they ring together $15+1=16$ times.
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