Question

Find two numbers if their Least Common Multiple, LCM is 100 and their Highest Common Factor, HCF is 5. Give two possible pairs of answers. ​

Answer 1

Step-by-step explanation:

Let H = HCF(A,B) and L = LCM(A,B)

Then A*B = L*H

Here L*H = 100*5 = 500

Also H <= A ,B <= L

So we need to find all A*B = 500, satisfying the above condition. This can be done using prime factorisation of 500.

Here 500 = 2^2 * 5^3

so possible values of A and B are

1 , 500

2, 250

4, 125

5,100

10,50

20,25

(assuming order doesn’t matter.)

so pairs satisfying given condition are → (20,25) and (100,5)

You can write a computer program in language of your choice to do it for other bigger numbers.