Question

Find the LCM and HCF of: 6hrs 4mins 30 secs & 2hrs 42 mins
Answer it correctly and don't send any rubbish unless I will report​

Answer 1

Answer:

First device beeps in every 30 min

Second device beeps in every 60 min

Third device beeps in every 90 min

Fourth device beeps in every 105 min

That means together they beep after how many minutes

We calculate LCM (30, 60, 90, 105) =

30=2x3x5

60=2²x3x5

90=2x3²x5

105=3x5x7

So, LCM= 2²x3²x5x7= 1260

ie, in 1260/60 = 21hrs they beep together

At 12 noon, all the devices beep together, Then after 21 hrs means.. it will be next day morning at 9am, these beep together again( as 12 noon to 12 midnight= 12 hrs. Then 9 hrs more, ie, 1am to 9am)

Ans : 9 am next day

JUSTIFICATION:

But now to justify this answer , we can explain as, second device is the only device which beeps only when the clock shows the whole figure time like 1 o'clock, 2 o'clock, 3 o'clock……… etc.

So we consider the common timing for all the devices only when the clock shows whole figure time. For first device too( other than fractional time) during every whole fig time it will beep.

Whole figure time for third device will be in every 3 hours, ie, only multiples of 3, like after12noon, 3pm, 6pm, 9pm, 12midnight, 3am, 6am, 9am……

Whole figure time for fourth device will be in every 7 hours, ie, after 12 noon, 7pm, 2am, 9am…..,

So the common time for all the four devices to beep next will be next day 9am