Chapter 6.4, Problem 14E

To determine

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

Answer to Problem 14E

The LCD is,

  $LCD=540$

Explanation of Solution

Given: The pair of denominators are,

  $\begin{array}{l}{D}_1=27\\ D_2=36\\ D_3=30\end{array}$

Calculation:

The denominators can be written as,

  $a=\frac{1}{27}+\frac{1}{36}+\frac{1}{30}$

Calculate the LCD,

  $\begin{array}{ccc}{D}_1& D_2& D_3\\ 27\times 1=27& 36\times 1=36& 30\times 1=30\\ 27\times 2=54& 36\times 2=72& 30\times 2=60\\ 27\times 3=81& 36\times 3=108& 30\times 3=90\\ ⋮& ⋮& ⋮\\ 27\times 20=540& 36\times 15=540& 30\times 18=540\end{array}$

We can see in the table, if we multiply 20 into 27, 15 into 36, and 18 into 30 then all the denominator becomes common. So, the LCD would be 540 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.