RELATION BETWEEN LCM -HCF (POST-14)

Good morning students !😊😊

Welcome to mathematics blog lesson.

Topic is -"Playing with numbers"

➧Copy the Explanation with examples in your MATHS NOTEBOOK

Today, by the end of the lesson you will be able to:

➤ explain the relation between H.C.F and L.C.M

➤ apply the formula of its relation to solve the sums. 

 COPY EVERYTHING  GIVEN BELOW IN YOUR MATH NOTEBOOK

Co-relation between H.C.F and L.C.M

Please have a look at the video that is given below. There is an interesting co-relation between H.C.F and L.C.M. of two numbers. The product of the H.C.F. and L.C.M. of any two numbers is always equal to the product of those two numbers. However the same is not applicable to three or more numbers. 

https://youtu.be/A4Z7GahjFWc  

These examples will now help you to understand even better. Do you realise that you are now slowly being able to understand Maths all by yourself.

Example: Let the two numbers be 4 and 6.

       H.C.F of (4,6) = 2     and       LCM of (4,6) = 12

Product of numbers = 4 x 6 = 24

Product of H.C.F and L.C.M = 2 x 12 = 24.

Thus, H.C.F. × L.C.M. = First number × Second number

        Or, First Number = H.C.F x L.C.M

                                      Second Number

        Or, H.C.F     =  First number × Second number

                                         L.C.M

        Or, L.C.M     = First number × Second number

                                         H.C.M

 Some Solved examples on the relationship between H.C.F. and L.C.M.:

   1. Highest common factor and lowest common multiple of two numbers are 18 and 1782 respectively. One number is 162, find the other.                               

Solution: We know, H.C.F. × L.C.M. = First number × Second number

            then we get,  18   x   1782   =  162  x   Second number

                           =>  18   x   1782   =  Second Number

                                       162

                Thus,  Second Number   =   32076   =  198.

                                                               162

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   2. If two numbers 3 and 12 have their LCM as 12, then what will be their H.C.F?

Solution: We know, H.C.F. × L.C.M. = First number × Second number

                                          H.C.F       =  First number × Second number

                                                                             L.C.M

                                   Thus,  H.C.F =  3 x 12   =  36  =  3.

                                                               12          12

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    3. Consider the numbers 24 and 60. Their H.C.F is 12. Find L.C.M.

Solution: We know, H.C.F. × L.C.M. = First number × Second number

                                   
                                           L.C.M     =  First number × Second number

                                                                             H.C.F

                                               L.C.M =       24 x 60   =  1440  =  120.

                                                                       12             12

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I Hope! you have understood the relation between H.C.F & L.C.M

Now, Practice the following questions :

1. Given that H.C.F of (306, 657) = 9, find L.C.M of (306, 657) .     
[Ans- 22,338]

2. The H.C.F and the L.C.M of two numbers are 825 and 25 respectively. If one of the two numbers is 275, find the other number.                       
 [Ans- 75]

       That's all for today

        Take Care 😊