Question

A two bells ring at an interval of 30 and 45 minutes. If the bells ring together at 1:00 pm at what time will they ring together . It is LCM question why ? Why it is LCM plz explain

Answer 1

Given:

• Two bells ringing at intervals of 30 and 45 minutes.
• They again rings at 1:00 pm

Find:

• At what time will they ring again together.

Solution:

we, find the least common factor of 30 and 45

$\underline{ \: \: \: 2|30,45|} \\ \underline{ \: \: \: 3|15,45|} \\ \underline{ \: \: \: \: 3|5,15 \:|} \\ \underline{ \: \: \: \: 5|5,5 \: \: |} \\ \: \: \: \: \: |1,1 \: \: \: \: |$

$: \to 2 \times 3 \times 3 \times 5$

$:\sf \to 2 \times 3 \times 3 \times 5 = 90mins$

Now,

$\sf : \implies 60mins = 1hr$

$\sf : \implies 1mins = \frac{1}{60} hr$

$\sf : \implies 90mins = \frac{1}{60} \times 90 = 1.5hr$

$\sf : \to 1pm + 1.5hr=2.5pm$

Hence, they rings together at 2.5pm