Question

Suppose a and b are positve integers such that LCM (a,b) = 90 and gcd (a,b) = 3. If b is three more than a, then what are the values of a and b?​

Answer 1

Step-by-step explanation:

As GCD (a,b) = 3 , let we consider, a=3x & b=3y , then LCM (a,b) = 3xy

Therefore 3xy = 90 , i.e xy = 30 . Now as given 3y - 3x =3

or , y - x = 1

or , y = x+1

Therefore x ( x+1) =30

or , x^2 + x - 30 = 0

solving we get x =- 6 , 5 , x = 5 acceptable because it is positive .

Therefore the numbers are a= 3 x 5 = 15 & b= 15 + 3 = 18