Download 3 __ 4 12 = 3 × 3 4 × 3 5 __ 8 = 5 × 8 × 40 1 __ 6 12 = 1 × 6 × 7 20 7

Least Common Denominator Find the least common denominator of two or
more fractions by finding the least common multiple of two or more numbers.
One Way Use a list.
Find the least common denominator of 3_4 and 1_6 . Use the least common
denominator to write an equivalent fraction for each fraction.
STEP 1
List nonzero multiples of the denominators. Find the least common multiple.
Multiples of 4: _______
Multiples of 6: _______
So, the least common denominator of 3_4 and 1_6 is
_.
STEP 2 Using the least common denominator, write an equivalent
fraction for each fraction.
Think: What number multiplied by the denominator of the
fraction will result in the least common denominator?
× 3 = ____
3
? =3
__ = ___
____
4 12 4 × 3
? =1
×
1 = ___
__
______
= ____
6
12
6×
least common denominator
3
__ can be rewritten as
__ can be rewritten as _ and 1
4
6
_.
Another Way Use prime factors.
7 . Then write an
Use prime factors to find a common denominator of 5_8 and __
20
equivalent fraction for each fraction.
STEP 1
Write each denominator as a product of its prime factors.
Prime factors of 8: 2 × 2 × 2
Think: Look for all prime factors that are
common to both numbers.
A common denominator of
5
_
8
and
7
__
20
is 2 × 2 × 2 × 5 = 40.
STEP 2 Write an equivalent fraction for each fraction.
× = ____
5
__ = 5
_____
40
8 8×
5
_
8
270
7 = _________
7 ×
___
= ____
20
can be rewritten as _ and
20 ×
7
__
20
40
can be rewritten as _.
© Houghton Mifflin Harcourt Publishing Company
Prime factors of 20: 2 × 2 × 5