PBCC 1 SLC Lake Worth Math Lab
STRATEGIES FOR FINDING THE
LEAST COMMON MULTIPLE (LCM)/LEAST COMMON DENOMINATOR (LCD)
The least common multiple (LCM) of a given set of numbers is the smallest positive number divisible
by the numbers in the set. For example, if we list the multiples of 4 and 6, we can see these numbers
share common multiples of 12, 24, 36, and 48 to name a few.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, …
Even though 24, 36 and 48 are multiples of 4 and 6, the LCM is 12 because 12 is the smallest number
divisible by 4 and 6.
When we need to find a common denominator for a given set of fractions, the LCM is called the least
common denominator (LCD). To find the LCD of a given set of fractions, check the denominators of
the fractions:
STRATEGIES
1) Do the smaller denominators divide the larger? If they do, the larger denominator is the LCD.
EXAMPLE 1: Find the LCD of 8
5
and,
2
1
,
4
3
Because 8 is divisible by 4 and 2, the LCD = 8.
2) Are the denominators prime or relatively prime numbers? (Prime numbers are numbers divisible
only by themselves and 1; relatively prime numbers share no common factor.) When the
denominators are prime or relatively prime, multiply the denominators to find the LCD.
EXAMPLE 2: Find the LCD of 2
1
and,
5
4
,
3
2
The denominators of the fractions are prime numbers. To find the LCD, multiply the denominators:
LCD = 2 • 3 • 5 = 30.
EXAMPLE 3: Find the LCD of 7
5
and
4
3
The denominators of the fractions are relatively prime numbers because they share no common
factors: 4 = 2 • 2 and 7 = 1 • 7. To find the LCD, multiply the denominators:
LCD = 4 • 7 = 28.
