To find the numbers in the given ratio, we need to consider the LCM (Least Common Multiple) of the two numbers. The LCM is the smallest multiple that is divisible by both numbers.

Let's assume the two numbers in the ratio are 3x and 5x, where x is a positive integer. We need to find the value of x.

Step 1: Finding the LCM
The LCM of two numbers can be found by multiplying the prime factors of the numbers, each raised to the maximum power it occurs.

Prime factorization of 3: 3
Prime factorization of 5: 5

The LCM of 3 and 5 is 3 * 5 = 15.

Step 2: Solving for x
Now that we have the LCM, which is 15, we can set up an equation to find the value of x.

3x * 5x = 15

15x^2 = 15

Dividing both sides by 15, we get:

x^2 = 1

Taking the square root of both sides, we have:

x = ±1

Since x needs to be a positive integer, we take x = 1.

Step 3: Finding the numbers
Substituting the value of x in the ratio, we get:

First number = 3 * 1 = 3
Second number = 5 * 1 = 5

So, the two numbers in the ratio 3:5 are 3 and 5.

Summary
- The LCM of the two numbers in the ratio 3:5 is 15.
- By solving the equation using the LCM, we find that the value of x is 1.
- Substituting the value of x in the ratio, we find that the two numbers are 3 and 5.

9 and 15 but 45 can be also their LCM .