Find the Least Common Denominator (LCD) of \(\frac{5}{4},\frac{2}{7}\). In other words, find the Least Common Multiple (LCM) of \(4,7\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 4
: 4, 8, 12, 16, 20, 24, 28, ...
Multiples of 7
: 7, 14, 21, 28, ...
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 7
: 7
Find the union of these primes.
\[2,2,7\]
Multiply these numbers: \(2\times 2\times 7=28\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{5\times 7}{4\times 7}-\frac{2\times 4}{7\times 4}\]
Simplify. Denominators are now the same.
\[\frac{35}{28}-\frac{8}{28}\]
Join the denominators.
\[\frac{35-8}{28}\]
Simplify.
\[\frac{27}{28}\]
Decimal Form: 0.964286
27/28
