Relationship between LCM and HCF.

 The following equation relates the LEAST COMMON MULTIPLE (LCM) and HIGHEST COMMON FACTOR (HCF) of any two numbers:-

(HCF)×(LCM) = (1st number)×(2nd number)

This relation is used to solve sums in the following situations:-

1) When the two numbers are given, and LCM is given and we are asked to find out the value of HCF.

2) When the two numbers are given and HCF is given and we are asked to find out the value of LCM

3) When LCM and HCF of two numbers is given and one of the two numbers is given and the second number is required to be found out.

Solved Example :- If the HCF and LCM of two numbers are 12 and 48 respectively and one of these numbers is 24 then find the value of the second number.

Solution :- Given- HCF = 12

                              -LCM = 48

                              - First number = 24

 Formula --

(HCF)×(LCM) = (1st number)×(2nd number)

Therefore,

12×48 = 24 × (second number)

Second number × 24 = 576

Second number = 576 ÷ 24

Second number = 24

Solve yourself  :-

-If two numbers 3 and 12 have their LCM as 12, then what will be their HCF?