Chapter 6.4, Problem 13E

To determine

Compare the least common denominator (LCD) from the exercise 1, 2, 3.

Answer to Problem 13E

The LCD is,

  $LCD=21$

  $LCD=72$

  $LCD=195$

Explanation of Solution

Given: The denominator pairs in exercise 1, 3, 5 are,

  $\begin{array}{l}{D}_1=7\\ D_2=21\end{array}$ , $\begin{array}{l}{D}_1=24\\ D_2=36\end{array}$ , $\begin{array}{l}{D}_1=13\\ D_2=15\end{array}$

Calculation:

The denominators can be written as,

  $\begin{array}{l}a=\frac{1}{7}+\frac{1}{21}\\ b=\frac{1}{24}+\frac{1}{36}\\ c=\frac{1}{13}+\frac{1}{15}\end{array}$

Calculate the LCD for $\begin{array}{l}{D}_1=7\\ D_2=21\end{array}$ ,

  $\begin{array}{cc}{D}_1& D_2\\ 7\times 1=7& 21\times 1=21\\ 7\times 2=14& \\ 7\times 3=21& \end{array}$

We can see in the table, if we multiply 3 into 7 and 1 into 21 then both the denominator becomes common. So, the LCD would be 21 because it is common after multiplication.

Then LCD for $\begin{array}{l}{D}_1=24\\ D_2=36\end{array}$ ,

  $\begin{array}{cc}{D}_1& D_2\\ 24\times 1=24& 36\times 1=36\\ 24\times 2=48& 36\times 2=72\\ 24\times 3=72& \end{array}$

We can see in the table, if we multiply 3 into 24 and 2 into 36 then both the denominator becomes common. So, the LCD would be 72 because it is common after multiplication.

Then LCD for $\begin{array}{l}{D}_1=13\\ D_2=15\end{array}$ ,

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

We can see in the table, if we multiply 15 into 13 and 13 into 15 then both the denominator becomes common. So, the LCD would be 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 LCD.