Question

The difference of lcm and hcf of two number is 1572 and thier sum of lcm and hcf is 1596.if one number is 144 than the other is

Answer 1

The other number will be 11/12

Answer 2

Solution :-

One of the two numbers is 144 (Given)

Let the other number be 'a'

Let L.C.M. of 144 and a be 'x' and let the H.C.F. of 144 and a be 'y' 

⇒ x + y = 1596 ............(1)

And 

⇒ x - y = 1572 ............(2)   

Adding both (1) and (2)

  x + y  = 1596
  x - y   = 1572
____________
 2x     =    3168
____________

⇒ 2x = 3168

⇒ x = 3168/2

⇒ x = 1584

Putting the value of x = 1584 in (1), we get

x + y = 1596

⇒ 1584 + y = 1596

⇒ y = 1596 - 1584

⇒ y = 12

So, L.C.M. of 144 and a = 1584

And,

H.C.F. of 144 and a = 12

We know that,

L.C.M. × H.C.F. = Product of the two numbers

⇒ 1584 × 12 = 144 × a

⇒ 144a = 1584 × 12

⇒ 144a = 19008

⇒ a = 19008/144

⇒ a = 132

So, the other number is 132

Answer.