The Least Common Denominator

Any common multiple works as a denominator, but the smallest one keeps the numbers small. Take $\frac{5}{6}+\frac{1}{8}$. The product $6\cdot 8$, which is 48, works: $\frac{40}{48}+\frac{6}{48}$ is $\frac{46}{48}$, and that still has to be simplified to $\frac{23}{24}$.

The least common multiple of 6 and 8 is 24. With it, $\frac{20}{24}+\frac{3}{24}$ is $\frac{23}{24}$ straight away, already in lowest terms. The LCM of the denominators is called the least common denominator, or LCD. It is the same LCM you found earlier in this section.

A quick way to find it: list the multiples of the bigger denominator until you reach one that the smaller denominator divides. Multiples of 8 are 8, 16, 24. 6 divides neither 8 nor 16, but it divides 24, so 24 is the LCD.