Four bells ring at intervals of $4, 6, 8$ and $14$ seconds. They start ringing simultaneously at $12.00$ O'clock. At what time will they again ring simultaneously?

12 h r 2 m i n . 48 s e c .

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12 h r 3 m i n .

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12 h r 23 m i n . 20 s e c .

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12 h r 3 m i n . 44 s e c .

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Solution

The correct option is A $12 h r 2 m i n . 48 s e c .$
$4 = 2 \times 2$
$6 = 2 \times 3$
$8 = 2 \times 2 \times 2$
$14 = 2 \times 7$
LCM of $4, 6, 8, 14 = 2 \times 2 \times 2 \times 3 \times 7 = 168 s e c o n d s$
$=$ Bells will ring again $2$ minutes $48$ seconds after $12$ O'clock
$= 12 h o u r s 2 m i n u t e s 48 s e c o n d s$ .

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