Chapter 6.4, Problem 5E

To determine

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

Answer to Problem 5E

The solution is,

  $LCD=195$

Explanation of Solution

Given: The pair of denominators are,

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

Calculation:

We may write the denominators in the form,

  $a=\frac{1}{13}+\frac{1}{15}$

Calculate the LCD,

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

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 21 because it is common after multiplication.

program:

clc
clear
close all
x=input('Enter the first denominator:');
y=input('Enter the second denominator:');
for i=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, we have defined both the denominators.
• The calculate the remainder.
• Then identify at which value remainder is zero.
• Then calculate the LCM.