Question

The HCF of two numbers is \[18\] and the product of two numbers is \[12960\] . Find the LCM of the two numbers.

Answer 1

Hint: For solving this particular problem , we have to consider the well-known relationship between HCF of the two number , their product and LCM of the two numbers that is ,
Product of the two numbers is equal to the product of HCF and LCM of the two numbers.
Or mathematically we can write,
Product of two numbers $ = HCF \times LCM$.

Formula Used:
Product of the two numbers is equal to the product of HCF and LCM of the two numbers.
Or mathematically we can write,
Product of two numbers $ = HCF \times LCM$ .

Complete step-by-step solution:
It is given that ,
HCF of the two numbers is equal to \[18\] ,
Product of the two numbers is equal to \[12960\] .
We have to find,
LCM of the two numbers.
As we know there exist a relationship between HCF of the two number , their product and LCM of the two numbers that is ,
Product of the two numbers is equal to the product of HCF and LCM of the two numbers.
Or mathematically we can write,
Product of two number $ = HCF \times LCM$ ,
Now substitute the given values in the above formula.
$ \Rightarrow 12960 = 18 \times LCM$
Or we can write,
$
   \Rightarrow LCM = \dfrac{{12960}}{{18}} \\
   \Rightarrow LCM = 720 \\
 $
Therefore , LCM of the two numbers is $720$ .

Note:
i) HCF gives the greatest common factor between two given numbers .
ii) LCM gives the least common factor between two given numbers.
iii) Product of the two numbers is equal to the product of HCF and LCM of the two numbers.