Find the Least Common Denominator (LCD) of \(\frac{3}{4},\frac{1}{8}\). In other words, find the Least Common Multiple (LCM) of \(4,8\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 4
: 4, 8, ...
Multiples of 8
: 8, ...
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 4
: 2, 2
Prime Factors of 8
: 2, 2, 2
Find the union of these primes.
\[2,2,2\]
Multiply these numbers: \(2\times 2\times 2=8\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{3\times 2}{4\times 2}+\frac{1}{8}\]
Simplify. Denominators are now the same.
\[\frac{6}{8}+\frac{1}{8}\]
Join the denominators.
\[\frac{6+1}{8}\]
Simplify.
\[\frac{7}{8}\]
Decimal Form: 0.875
7/8
