Question

If the sum of squares of lcm & hcf of twopositive numbers is 3609 and their lcm is 57more than their hcf, then the product of twonumber's is -

Answer 1

Answer:

Let x and y be LCM and HCF of numbers A and B.

According to the given conditions.

LCM+HCF=x+y=3609. ....(1).

x=57+y.  ......(2).

putting equation (2) in equation (1) we get

57+y+y=3609.

57+2y=3609.

By subtracting 57 from both sides we get

2y=3609-57

2y=3552.

Dividing by 2 on both sides we get

y=1776.

put value of y in equation (2) to get

x=57+1776=1833.

Now we know that

LCM *HCH=A*B

so using above formula we get

product of numbers A and B=A*B=x*y=1833*1776=3255408.

So product of numbers is 3255408.

Step-by-step explanation: