Find the Least Common Denominator (LCD) of \(\frac{37}{12},\frac{7}{8}\). In other words, find the Least Common Multiple (LCM) of \(12,8\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 12
: 12, 24, ...
Multiples of 8
: 8, 16, 24, ...
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 8
: 2, 2, 2
Find the union of these primes.
\[2,2,2,3\]
Multiply these numbers: \(2\times 2\times 2\times 3=24\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{37\times 2}{12\times 2}+\frac{7\times 3}{8\times 3}\]
Simplify. Denominators are now the same.
\[\frac{74}{24}+\frac{21}{24}\]
Join the denominators.
\[\frac{74+21}{24}\]
Simplify.
\[\frac{95}{24}\]
Convert to mixed fraction.
\[3\frac{23}{24}\]
Decimal Form: 3.958333
mixed(3,23/24)
