Bells

[greatwhiteshark]

A bell rings every 2 hours, a second bell rings every 3 hours, and a third bell rings every 4 hours. If all 3 bells ring at 9:00 AM., at what time will all 3 bells next ring?

 

[Denis]

2,4,6,8,10,12...
3,6,9,12,15,18...
4,8,12,16,20,24...

 

[soroban]

Hello, greatwhiteshark!

A bell rings every 2 hours, a second bell rings every 3 hours, and a third bell rings every 4 hours.
If all 3 bells ring at 9:00 AM, at what time will all 3 bells next ring?

To baby-talk through Denis' hint:

Bell 1: .9a, 11a, 1p, 3p, 5p, 7p, 9p, 11p, 1a, 3a, 5a, 7a, 9a, . . .
Bell 2: .9a, 12n, 3p, 6p, 9p, 12m, 3a, 6a, 9a, . . .
Bell 3: .9a, 1p, 5p, 9p, 1a, 5a, 9a, . . .


The short method:
. . The Least Common Multiple of 2, 3, 4 is <u>12</u>.
. . The bells will ring together every 12 hours.

 

[greatwhiteshark]

okay

This was a tricky question. I am glad to find help on this site,
especially from Soroban.