How weather the given question is …

<i>whenever you are required to find a number that is </i><i>divisible</i><i> by more than one number, you have to find LCM.</i>

<i>whenever you are required to find a number that </i><i>completely divides</i><i> more than one number, you have to find HCF.</i>

Coming to illustrative examples :

<i>LCM</i>

<i>Three traffic signals change from Red to Green in 10, 15 & 20 seconds respectively. After how much time will all three signals together become Green ?</i>

The three traffic signals will change from Red to Green as follows ( in seconds ):

First : 10,20,30,40,50,60,70,80 …..

Second : 15,30,45,60,75,90 …

Third : 20,40,60,80 …

It is clear the three signals will flash Green together after 60 seconds. Now , this 60 is completely <i>divisible</i> by 10, 15 & 20 and LCM(10, 15 , 20) is 60, hence the problem was of finding LCM.

<i>HCF</i>

<i>Square towels has to be cut from a piece of cloth measuring 16m x 20m. What is the minimum number of towels that can be cut so that there is no wastage ?</i>

The towels are square and length is equal to width. Since there should be no wastage, the edge of the towel should exactly divide the length & breadth of the piece of cloth. The dimension of the towel is that highest number which completely divides 16 & 20. So, here we have a case of HCF.

HCF(16,20) = 4

So, the dimension of towel is 4m x 4m

The minimum number of towels possible is (16 x 20 )/ (4 x 4) = 20.