Question

there are 4 mobile phone in a house at 5 am.All the 4 mobile phone will ring together.
there after the first one rings every 15 minutes, second one rings every 20 minutes, third one rings every 25 minutes and 4th one rings every 30 minutes.After what time all the 4 mobile will ring together again?

options
11 a.m
10 a.m
10.30 a.m
11.30 a.m

please explain step by step​

Answer 1

The time at which all 4 mobile phones will ring together is 10 a.m

Solution:

It is given that there are 4 mobile phones in a house at 5 am. All the 4 mobile phones will ring together

First one rings every 15 minutes

Second one rings every 20 minutes

Third one rings every 25 minutes

4th one rings every 30 minutes.

From the given data we understand that we need to find the exact time after which all 4 mobiles will ring together, even though they have different ringing intervals.

The only way we can determine that is by taking an LCM( lowest common multiple) of the 4 ringing intervals.

The ringing intervals are 15, 20, 25 and 30

Finding L.C.M of 15, 20, 25 and 30:

List all prime factors for each number

Prime factors of 15 = $3 \times 5$

Prime factors of 20 = $2 \times 2 \times 5$

Prime factors of 25 = $5 \times 5$

Prime factors of 30 = $2 \times 3 \times 5$

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3, 5, 5

Multiply these factors together to find the LCM.

$LCM = 2 \times 2 \times 3 \times 5 \times 5 = 300$

Hence all the 4 phones will ring together 300 mins after 5a.m.

300 minutes = 5 hours

So 5 a.m + 5 hours = 10 a.m

Therefore, the time at which all 4 mobile phones will ring together is 10a.m

Learn more about L.C.M

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