Find the Least Common Denominator (LCD) of \(\frac{3}{5},\frac{1}{5},\frac{3}{20}\). In other words, find the Least Common Multiple (LCM) of \(5,5,20\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 5
: 5, 10, 15, 20, ...
Multiples of 5
: 5, 10, 15, 20, ...
Multiples of 20
: 20, ...
Find the smallest number that is shared by all rows above. This is the LCM.
LCM = \(20\)
Method 2: By Prime Factors
List the prime factors of each number.
Prime Factors of 5
: 5
Prime Factors of 5
: 5
Prime Factors of 20
: 2, 2, 5
Find the union of these primes.
\[2,2,5\]
Multiply these numbers: \(2\times 2\times 5=20\). This is the LCM.