Question

hcf of two numbers, each consisting of four digits, is 103 and their lcm is 19261. the difference of the numbers is (a) 6/8 (b) 5/9 (c) 5/8 (d) 4/8

Answer 1

Answer:

618

Step-by-step explanation:

Given hcf of two numbers, each consisting of four digits, is 103 and their lcm is 19261. the difference of the numbers is

Let the two numbers be x and y and two numbers will be 103 x and 103 y

since the numbers x and y are prime to each other.

Now we know that according to question

  103 xy = lcm that is 19261

 So 103 xy = 19261

      xy = 19261 / 103

       xy = 187

 So x will be 11 and y will be 17 since 11 x 17 = 187

Now 103 x 11 = 1133 and 103 x 17 = 1751

So the numbers are 1133 and 1751. Now the difference of the numbers are 1751 - 1133 = 618

Answer 2

Answer:

hcf of two numbers, each consisting of four digits, is 103 and their lcm is 19261. the difference of the numbers is 618

Step-by-step explanation:

Let one number be 103a  & another number 103b

as 103a & 103b are 4 digit numbers so

98 > a , b > 9  a & b are distinct number

103a & 103b = LCM * HCF

=> 103 a * 103 b = 103 * 19261

=> ab = 187

a & b can be 11 & 17

Difference between numbers

103 * (17 -11)

= 103 * 6

= 618

option a is correct