Question

The sum of two numbers is 135 and their H.C.F. is 27. If their L.C.M. is 162, the numbers are?
Pls send step-by-step answer

Answer 1

The correct option is 81, 54
H.C.F. of two numbers is 27.
So let the numbers are 27a and 27b
Now, 27a + 27b = 135
⇒
a+ b = 5 ...(i)
Also, Product of two numbers = H.C.F. of the numbers
×
L.C.M. of two numbers
27a
×
27b = 27
×
162.
⇒
ab = 6 ...(ii)
(
a
−
b
)
2
=
(
a
+
b
)
2
−
4
a
b

(
a
−
b
)
2
=
5
2
−
(
4
×
6
)

⇒
a - b = 1 ...(iii)
Solving (i) and (iii) we get
a = 3, b = 2
So, numbers are 27
×
3, 27
×
2 i.e., 8