Find the Least Common Denominator (LCD) of \(\frac{1}{12},\frac{1}{6}\). In other words, find the Least Common Multiple (LCM) of \(12,6\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 12
: 12, ...
Multiples of 6
: 6, 12, ...
Find the smallest number that is shared by all rows above. This is the LCM.
Method 2: By Prime Factors
List the prime factors of each number.
Prime Factors of 12
: 2, 2, 3
Prime Factors of 6
: 2, 3
Find the union of these primes.
\[2,2,3\]
Multiply these numbers: \(2\times 2\times 3=12\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{1}{12}+\frac{1\times 2}{6\times 2}\]
Simplify. Denominators are now the same.
\[\frac{1}{12}+\frac{2}{12}\]
Join the denominators.
\[\frac{1+2}{12}\]
Simplify.
\[\frac{3}{12}\]
Simplify.
\[\frac{1}{4}\]
Decimal Form: 0.25
1/4
