Find the Least Common Denominator (LCD) of \(\frac{9}{10},\frac{4}{15}\). In other words, find the Least Common Multiple (LCM) of \(10,15\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 10
: 10, 20, 30, ...
Multiples of 15
: 15, 30, ...
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 10
: 2, 5
Prime Factors of 15
: 3, 5
Find the union of these primes.
\[2,3,5\]
Multiply these numbers: \(2\times 3\times 5=30\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{9\times 3}{10\times 3}-\frac{4\times 2}{15\times 2}\]
Simplify. Denominators are now the same.
\[\frac{27}{30}-\frac{8}{30}\]
Join the denominators.
\[\frac{27-8}{30}\]
Simplify.
\[\frac{19}{30}\]
Decimal Form: 0.633333
19/30
