Question

An alarm beeps every $3$ hour, and another alarm beeps every $12$ hour. If they beep at $00:00$ hour, at what time will they again beep together?

• A. $06:00$
• B. $12:00$

Answer 1

The correct option is B $12:00$

$1^{st}$ alarm deeps in an interval of $3$ hours, and the $2^{nd}$ alarm deeps in an interval of $12$ hours.

First, they beep at $00:00$ hour.
Next, they will beep together at a time, which is the least common multiple of $3$ and $12$ hours.

$3$ is itself a prime number.
Using prime factorization,
$12=2^2\times 3$

$\therefore$ LCM $=3\times 2^2=12$

$\therefore$ They will beep together after $12$ hours, i.e., $12:00$ hours.