Chapter 4.4, Problem 1E

To determine

To find terms least common multiple ad least common denominator related.

Answer to Problem 1E

The LCD and the LCM require the same math process: Finding a common multiple of two (or more) numbers. The only difference between LCD and LCM is that the LCD is the LCM in the denominator of a fraction. So, one could say that least common denominators are a special case of least common multiples.

Explanation of Solution

Calculation:

Let's check the following fractions:

  $\frac{1}{2},\frac{2}{3},\frac{5}{6}$

To find the lowest common denominator of the fractions , find the lowest common multiple of the fractions' denominators:

  $lcd\left(\frac{1}{2},\frac{2}{3},\frac{5}{6}\right)=lcm(2,3,6)$

To calculate the LCM , find the lowest number which can be obtained by multiplying those numbers.

This number is 6 because 2 $\times$ 3 and 3 $\times$ 2 multiply to get 6.