Question

Three alarm clocks ring at intervals at 4,12 and 20 minute respectively. If they start ringing together after how much time will they next ring together?

Answer 1

Hint: To find the time taken for all the three alarm clocks to ring together, we will find the LCM of 4, 12 and 20. LCM of these are found by looking at their divisibility by prime numbers. The result of the LCM of 4, 12 and 20 will be the required answer.

Complete step-by-step answer:
We are given that three alarm clocks ring at intervals at 4,12 and 20 minute respectively. Also all these ring at same time. We have to find after how much time they will next ring together.
Since all the three clocks ring together, we have to find their LCM.
Let us take the LCM of 4, 12 and 20 using prime factorization method. LCM of these are found by looking at their divisibility by prime numbers.
$\begin{align}
  & 2\left| \!{\underline {\,
  4,12,20 \,}} \right. \\
 & 2\left| \!{\underline {\,
  2,6,10 \,}} \right. \\
 & 3\left| \!{\underline {\,
  1,3,5 \,}} \right. \\
 & 5\left| \!{\underline {\,
  1,1,5 \,}} \right. \\
 & \text{ 1,1,1} \\
\end{align}$
Thus, we found the LCM of 4, 12 and 20 to be $2\times 2\times 3\times 5=60$ .
Hence, the three clocks will ring together after 60 minutes or 1 hour.

Note: You may take HCF instead of LCM. We took LCM as we have to find the very next time at which the clocks will ring together. You can follow any method to find the LCM. You can use even the factor tree method. You make mistakes by adding 4, 12 and 20.