Chapter 6.4, Problem 12E

To determine

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

Answer to Problem 12E

The LCD is,

  $LCD=8$

Explanation of Solution

Given: The pair of denominators are,

  $\begin{array}{l}{D}_1=2\\ D_2=8\end{array}$

Calculation:

The denominators can be written as,

  $a=\frac{1}{2}+\frac{1}{8}$

Calculate the LCD,

  $\begin{array}{cc}{D}_1& D_2\\ 2\times 1=2& 8\times 1=8\\ 2\times 2=4& \\ 2\times 3=6& \\ 2\times 4=8& \end{array}$

We can see in the table, if we multiply 4 into 2 and 1 into 8 then both the denominator becomes common. So, the LCD would be 8 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.