Question

In a school, there are two bells, one in the primary school and the other in the secondary school. Both the bells ring after every class. The primary school has classes 45 minutes each whereas the secondary school has classes every 1 hour. Find when both the bells ring at the same time again if both classes start at the same time?

• A. 1 hour
• B. 2 hours
• C. 3 hours
• D. 4 hours

Answer 1

The correct option is C

3 hours

Since the bells have to ring together, we need to find the LCM of 45 minutes and 60 minutes.
$45=3^2\times 5$
$60=2^2\times 3\times 5$
Therefore, LCM = $2^2\times 3^2\times 5=180$

1 hour = 60 minutes
Therefore, 180 minutes = $\frac{180}{60}$= 3 hours

After 3 hours, both the bells will ring together if both classes start at the same time.