Question

The product of two numbers is 20736 and their HCF is 24. Find their LCM.

Answer 1

Hint: The product of two numbers is always equal to the product of their LCM and HCF, where LCM stands for lowest common factor and HCF is the highest common factor. Use this concept to get the answer.

Complete Step-by-Step solution:
As we know the multiplication of H.C.F and L.C.M of the two numbers is the product of two numbers.
Now it is given that the product of two numbers is 20736.
And the H.C.F of two numbers is 24.
Then we have to find out the L.C.M value of the product of two numbers.
So according to above information we have,
$ \Rightarrow H.C.F \times L.C.M = 20736$
$ \Rightarrow L.C.M = \dfrac{{20736}}{{H.C.F}}$
Now substitute the value of H.C.F we have,
$ \Rightarrow L.C.M = \dfrac{{20736}}{{H.C.F}} = \dfrac{{20736}}{{24}} = 864$
So 864 is the required L.C.M of the product of two numbers.

Note: Whenever we face such types of problems the key concept will solemnly base upon the relation between the product of numbers and their L.C.M and H.C.F. In some advanced questions the L.CM and H.C.F may have to be evaluated so directly from the factors of such numbers. This will help to get on the right track to reach the answer.