Ratio Numbers LCM Calculation

Let the two numbers be represented based on their given ratio of 1:7. We can express these numbers as $k$ and $7k$, where $k$ is a common factor.

LCM Relationship Explained

The Least Common Multiple (LCM) of two numbers $a$ and $b$ is the smallest positive integer that is divisible by both $a$ and $b$. For numbers $k$ and $7k$, their LCM is $7k$. This is because $7k$ is divisible by $k$ (result is 7) and by $7k$ (result is 1).

Calculating the Common Factor

We are given that the LCM of the two numbers is 721. Using the relationship derived above:

$7k = 721$

To find the value of $k$, we divide both sides of the equation by 7:

$k = \frac{721}{7}$

$k = 103$

Determining the Numbers

Now that we have the value of $k$, we can find the two numbers:

• First number: $k = 103$
• Second number: $7k = 7 \times 103 = 721$

Sum of Numbers Calculation

The question asks for the sum of these two numbers. We add the numbers found:

Sum = $103 + 721$

Sum = $824$

Thus, the sum of the two numbers is 824.