Factors of 12 and 20:
12 {1, 2, 3,
4,
6, 12}
20 {1, 2,
4,
5, 10, 20}
The greatest common factor is 4 (they do have 1 and 2 in common, but the
greatest factor is best).
Least Common Denominator
The
least common denominator
(LCD) is the smallest multiple that two
numbers share. Determining the LCD is an essential step in the addit
ion,
subtraction, and ordering of fractions.
Example 1
Find the LCD for
and .
Steps
1. List the multiples (multiplication tables) of each denominator
.
β’
4: 4 Γ 1 = 4, 4 Γ 2 = 8, 4 Γ 3 = 12, 4 Γ 4 = 16, 4 Γ 5 = 20, 4 Γ 6 = 24, 4 Γ 7 = 28, 4 Γ 8 =
32, 4 Γ 9 = 36, 4 Γ 10 = 40
β’
4 {4, 8, 12, 16, 20, 24, 28, 32, 36, 40}βthis will be the standard form throughout
for listing multiples.
β’
9 {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
2. Compare each for the least common multiple.
β’
4 {4, 8, 12, 16, 20, 24, 28, 32,
36,
40}
β’
9 {9, 18, 27,
36,
45, 54, 63, 72, 81, 90}
3. The LCD between 4 and 9 is 36 (4 Γ 9 = 36 and 9 Γ 4 = 36).
Example 2
Find the LCD for
and .
Steps
1. List the multiples of each denominator, and find the common multi
ples.
β’
12 {12,
24,
36, 48, 60, 72, 84, 96, 108, 120}
β’
8 {8, 16,
24,
32, 40, 48, 56, 64, 72, 80}
2. The LCD between 12 and 8 is 24 (12 Γ 2 = 24 and 8 Γ 3 = 24).
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