Suppose a and b are positive 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?

Given:

LCM(a,b) = 90 and GCD(a,b) = 3.

b is three more than a.

To find:

The values of a and b.

Solution:

We have,

LCM(a,b) = 90

GCD(a,b) = HCF(a,b) = 3

According to the question,

If a and b are two positive integers, then

Splitting the middle terms, we get

Using zero product property, we get

and

and

a is a positive integer so it cannot be negative. So, a=15.

Now,

Therefore, the value of a is 15 and the value of b is 18.