Chapter 6.4, Problem 7E

To determine

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

Answer to Problem 7E

The solution is,

  $LCD=72$

Explanation of Solution

Given: The pair of denominators are,

  $\begin{array}{l}{D}_1=24\\ D_2=36\end{array}$

Calculation:

We may write the denominators in the form,

  $a=\frac{1}{24}+\frac{1}{36}$

Calculate the LCD,

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

We can see in the table, if we multiply 3 into 24 and 2 into 36 then both the denominator becomes common. So, 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:');
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, we have defined both the denominators.
• The calculate the remainder.
• Then identify at which value remainder is zero.
• Then calculate the LCM.