Question

How can we know that in a particular question we have to find HCF or LCM?

Answer 1

Avoid the term “TRICK” like the plague. It is misleading and is used by very many coaching institutes to lure gullible students to them. There is nothing called TRICK or SHORTCUT in mathematics.

Having said that, let us talk about the problem at hand. It is very easy if we know the meaning of LCM and HCF.

Least Common Multiple, also called LCM is that smallest number which is completely divisible by a given set of numbers. For example, 30 is completely divisible by 5, 10 & 15 and hence is the LCM of 5,10 & 15. There is no number less than 30 that can boast the same.

So, whenever you are required to find a number that is divisible by more than one number, you have to find LCM.

Highest Common Factor, also called HCF, is that highest number that completely divides a given set of number. For example, 25 divides 50, 75, 100, 125, 725, 950. Since there is NO number greater than 25 that divides the given set of numbers, we call 25 as the Highest Common Factor or HCF.

So, whenever you are required to find a number that completely divides more than one number, you have to find HCF.

Coming to illustrative examples :

LCM

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 ?

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 divisible by 10, 15 & 20 and LCM(10, 15 , 20) is 60, hence the problem was of finding LCM.

HCF

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 ?


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.