Question

The sum of two numbers is 119, their hcf & lcm are 17 & 170

Answer 1

Hey there !

Solution:

Your question is incomplete. The question is to find the two numbers.

Let the numbers be x and y

=> x + y = 119  => Equation 1

Also we know that HCF * LCM = 17 * 170

=> xy = 2890

=> x = 2890 / y  => Equation 2

Substituting Equation 2 in Equation 1, we get,

=> 2890 / y + y = 119

=> 2890 + y² / y = 119

=> y² + 2890 = 119y

=> y² - 119y + 2890

=> y² - 34y - 85y + 2890

=> y ( y - 34 ) -85 ( y - 34 ) = 0

=> ( y - 85 ) ( y - 34 ) = 0

=> y = 85, 34

Now Case 1:

Let y = 85

=> x = 2890 / y = 2890 / 85 = 34

Case 2:

Let y = 34

=> x = 2890 / y = 2890 / 34 = 85

Hence the numbers are 34 and 85.

Hope my answer helped !