Question

$3$ bells in boothnath temple toll at the interval of $48,72,$and $108$ seconds .If they have tolled all together at $6:00$ AM then after after how many seconds all the bells will tolled together.

Answer 1

Here, we have to find how many seconds all the bells will tolled together.

$\Rightarrow$ $48=2\times 24$

$=2\times 2\times 12$

$=2\times 2\times 2\times 6$

$=2\times 2\times 2\times 2\times 3$

$=2^4\times 3$

$\Rightarrow$ $72=2\times 36$

$=2\times 2\times 18$

$=2\times 2\times 2\times 9$

$=2\times 2\times 2\times 3\times 3$

$=2^3\times 3^2$

$\Rightarrow$ $108=2\times 54$

$=2\times 2\times 27$

$=2\times 2\times 3\times 9$

$=2\times 2\times 3\times 3\times 3$

$=2^2\times 3^3$

$\Rightarrow$ $L.C.M$ of $48,72$ and $108$ $=2^4\times 3^3$

$=432$

$\therefore$ The required answer is $432.$