Question

if the sum of two number is 27 and their hcf and lcm are 3 and 60 respectively the

Answer 1

hope this helps you ....

Answer 2

Answer:

The numbers are 12 and 15

Step-by-step explanation:

Let the two numbers be a and b

According to question, the sum of two numbers is 27

⇒ a + b = 27

Value of b from above equation

b = 27 - a

Also, we are given LCM = 60 and HCF = 3

We know ,

LCM * HCF = Product of two numbers

LCM * HCF = a * b

Substituting the value of HCF , LCM and b from above,

60 * 3 = a * ( 27 - a )

180 = 27 a - a²

a² - 27a + 180 = 0

a² - 15a - 12a + 180 = 0

a ( a - 15 ) - 12 ( a - 15 ) = 0

( a - 15 ) ( a - 12 ) = 0

Taking ( a - 15 ) = 0

a = 15

Taking ( a - 12 ) = 0

a= 12

Values of a can be 15 or 12

Now,

b = 27 - a

For a = 15 , b = 27  - 15 = 12

For a = 12 , b = 27 - 12 = 15

Hence the numbers are  12 and 15