Question

# A light blinks after every $3$ seconds, another light blinks after every $5$ seconds. How many times do they blink together in half an hour?

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Solution

## Step 1: Find the LCM of $3$ and $5$To find how many times they blink together in half an hour, we take the LCM of $3$ and $5$$LCM\left(3,5\right)=15$ secStep 2: Find the number of times they blink together in half an hour$\begin{array}{rcl}\frac{1}{2}\mathrm{hour}& =& 30\mathrm{min}\\ & =& \frac{3600}{2}\mathrm{sec}\\ & =& 1800\mathrm{sec}\end{array}$Number of times they blink together in $30$ mins$=\frac{1800}{15}=120$Hence, both the lights blink 120 times in the given period of half an hour.

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