# What is the relationship between LCD and LCM?

Apr 15, 2016

Lowest common denominator is the lowest common multiple of the fractions' denominators.

#### Explanation:

Lowest common denominator is the lowest number to which all the fractions can be expanded, so it is the lowest common multiple of all denominators.

Example:

Let's check the following fractions:

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

To find the lowest common denominator of the fractions we haveto find the lowest common multoiple of the fractions' denominators:

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

To calculate the $\lcm$ we have to find the lowest number which can be obtained by multiplying those numbers.
This number is $6$ because we can multiply $2 \cdot 3$ and $3 \cdot 2$ to get $6$