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what is difference between H.C.F and L.C.M with examples.
why do we use HCFand LCM .

Dear Student,

Please find below the solution to the asked query:

We can clearly see the difference between these terms by their full form :

H.C.F. stands for highest common factor .

And

L.C.M.  stands for lowest common multiple

For example we have number :  12 ,  60 and 84 

Then first we make prime factors of these numbers , As :

12 = 2 × 2 × 3 ,

60 =  2 × 2 × 3 × 5

And

84 =  2 × 2 × 3 ×  7

Then,

H.C.F. ( 12 ,  60  and 84 ) =  2 × 2 × 3  =  12   

And

L.C.M. =  2 × 2 × 3 × 5 × 7 = 420                                    

We use these concepts according to nature of given query that you can easily distinguish after practise these type of questions and if you have any specific query then get back to us so that we could help you precisely . 

Regards

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View Full Answer
HCF means highest common factor and LCM means lowes common multiple.
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Among all the practical uses of LCM and hcf,those which I found most fascinating are:-

LCM:- suppose you and your girlfriend's claases are at hand,and the bells of each others classes get heared by you both.

Your bell rings after some particular intervals and your girl's bell also ring after some different intervals.Also,you both can meet each other only if bells of you both have rung simultaneously. So this situation of meeting of you both can easily be solved by using the LCM.

HCF:- suppose that you have four buckets of 14 ltr,28,35 and 49 ltr,and you have to use a container of the largest volume with which all the bucket's water could be measured exactly.

This situation can easily be handled using gcd or hcf

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