Find the Least Common Denominator (LCD) of \(\frac{99}{23},\frac{79}{37}\). In other words, find the Least Common Multiple (LCM) of \(23,37\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 23
: 23, 46, 69, ... , 805, 828, 851, ...
Multiples of 37
: 37, 74, 111, ... , 777, 814, 851, ...
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 23
: 23
Prime Factors of 37
: 37
Find the union of these primes.
\[23,37\]
Multiply these numbers: \(23\times 37=851\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{99\times 37}{23\times 37}+\frac{79\times 23}{37\times 23}\]
Simplify. Denominators are now the same.
\[\frac{3663}{851}+\frac{1817}{851}\]
Join the denominators.
\[\frac{3663+1817}{851}\]
Simplify.
\[\frac{5480}{851}\]
Convert to mixed fraction.
\[6\frac{374}{851}\]
Decimal Form: 6.439483
mixed(6,374/851)
