Please help me understand the solution of this question!

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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?

Seems like you made a Fencepost error. – Kyan Cheung Dec 12 '20 at 17:23 — Kyan Cheung, Dec 12 '20 at 17:23

score 3 · Accepted Answer · answered Dec 12 '20 at 17:25

3

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.

answered Dec 12 '20 at 17:25

Parcly Taxel

103,344

Please strive not to post more dupe answers to FAQs. Rather, please help organize and improve prior answers. – Bill Dubuque Dec 12 '20 at 17:33
@BillDubuque I can't. The other answers already are organised. – Parcly Taxel Dec 12 '20 at 18:09
Presumably you can resist answering dupes, and instead locate and link to dupes, and post answers in the dupes if you have anything novel to add. – Bill Dubuque Dec 12 '20 at 18:30

Please help me understand the solution of this question!

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