CLASS-5
RELATION BETWEEN HCF & LCM

IMPORTANT RELATION BETWEEN HCF & LCM

Please remember a very important fact, that is –

Multiplication of HCF & LCM of two given numbers is equal to the multiplication of the same two numbers.

HCF x LCM = Product of two given numbers or

HCF x LCM = 1^st Number x 2^nd Number

                   HCF x LCM                                    HCF x LCM

1^st Number = ---------------  OR  2^nd Number = --------------- 

                  2^nd Number                                     1^st Number

Now, for example, we would like to find HCF & LCF findings from the same two numbers for validating the above fact.         (Ans.)

1)  Find HCF & LCM of 84 & 24 and validate.

HCF = 2 x 2 x 3 = 12  and

LCM = 2 x 2 x 3 x ( 7 x 2 ) = 168

As per the law to validate the above formula –

HCF x LCM = 1^st Number x 2^nd Number

So, HCF x LCM = 12 x 168 =  2016

And, 1^st Number x 2^nd Number = 84 x 24 = 2016,

So, above calculation validate that - HCF x LCF = 1^st Number x 2^nd Number.   (Ans.)

 

2)  Find HCF & LCM of 120 & 84 and validate.

HCF = 2 x 2 x 3 = 12  and

LCF = 2 x 2 x 3 x ( 10 x 7 ) = 840

As per the law to validate the above formula –

HCF x LCM = 1^st Number x 2^nd Number

So, HCF x LC = 12 x 840 =  10080

And, 1^st Number x 2^nd Number = 120 x 84 = 10080,

So, above calculation validate that - HCF x LCF = 1^st Number x 2^nd Number.       (Ans.)