Chapter 6.4, Problem 10E

To determine

Calculate the least common denominator (LCD) for the given pair of denominator values.

Answer to Problem 10E

The LCD is,

  $LCD=195$

Explanation of Solution

Given: The pair of denominators are,

  $\begin{array}{l}{D}_1=13\\ D_2=15\end{array}$

Calculation:

The denominators can be written as,

  $a=\frac{1}{13}+\frac{1}{15}$

Calculate the LCD,

  $\begin{array}{l}\begin{array}{cc}{D}_1& D_2\\ 13\times 1=13& 15\times 1=15\\ 13\times 2=26& 15\times 2=30\\ 13\times 3=39& 15\times 3=45\end{array}\\ ⋮\\ \begin{array}{cc}13\times 15=195& 15\times 13=195\end{array}\end{array}$

We can see in the table, if we multiply 15 into 13 and 13 into 15 then both the denominator becomes common. So, LCD is 195 because it is common after multiplication.

program:

clc
clear
close all
x=input('Enter the first denominator:');
y=input('Enter the second denominator:');
fori=1:y
if (rem(x,i)==0 && (rem(y,i)==0))
        s=i;
end
end
z=x*y/s;
disp('LCD')
disp(z)

Query:

• First, define both the denominators.
• Then calculate the remainder.
• Identify the value at which remainder is zero.
• Then calculate the LCM.