Chapter 6.4, Problem 2E

To determine

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

Answer to Problem 2E

The solution is,

  $LCD=21$

Explanation of Solution

Given: The pair of denominators are,

  $\begin{array}{l}{D}_2=21\\ D_1=7\end{array}$

Calculation:

We may write the denominators in the form,

  $a=\frac{1}{21}+\frac{1}{7}$

Calculate the LCD,

  $\begin{array}{cc}{D}_2& D_1\\ 7\times 1=7& 21\times 1=21\\ 7\times 2=14& \\ 7\times 3=21& \end{array}$

We can see in the table, if we multiply 3 into 7 and 1 into 21 then both the denominator becomes common. So, 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.