#### Transcript Fraction IX Least Common Multiple Least Common Denominator

```Fractions
Denominators
LCM & GCF
Common Multiple

A number that is a multiple
of two or more numbers.
Some multiples of 3 & 6
6, 12, 18, 24, 30, 36, 42
Least Common Multiple

The smallest common multiple
of a set of two or more
numbers.
5 = 5, 10, 15, 20, 25, 30
6 = 6, 12, 18, 24, 30, 36
Shortcut for Finding the Least
Common Denominator or Least
Common Multiple
Check to see if the smaller denominator
divides evenly into the larger denominator.
If it does, use the larger denominator for
1
3
1
+ 9
3 will divide evenly into 9,
so 9 is your LCD or LCM.
With Unlike Denominators

Find the multiples of each
denominator.
1
5 = 5, 10, 15, 20, 25, 30
1
+10 = 10, 20, 30, 40, 50
With Unlike Denominators

Compare the lists of multiples.
Circle the common multiples
between the two lists.
1
5 = 5, 10, 15, 20, 25, 30
1
+10 = 10, 20, 30, 40, 50
With Unlike Denominators

Use the lowest common
multiple as the denominator.
1
5 = 5, 10, 15 ,20 ,25 ,30
1
+10 = 10, 20, 30, 40, 50
With Unlike Denominators

This number is also called the
least common denominator.
1
5 = 5, 10, 15 ,20 ,25 ,30
1
+10 = 10, 20, 30, 40, 50
With Unlike Denominators

Rewrite the fractions using the
least common denominator or
least common multiple.
1
5
1
+10
10
10
With Unlike Denominators
Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
You
know
that
1/10
1
is
equal
to
1/10
so
5
10
Put
a
1
over
the
1
1
Bottom
10.
+10
10

With Unlike Denominators
Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
To
find
the
top
1
number,
yourself
5
10
what
do
you
multiply
1
1
the
5
by
to
get
10.
+10
10

With Unlike Denominators
Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
That’s right 2. Since
you are looking for
1x 2 =
equivalent fraction
5 x 2 = 10 theyou
know the top
1
1 number must also be
+10
10
multiplied by 2.

With Unlike Denominators

Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
1 x 2 = 2 To find the top number
just multiply 2 x 1 to
5 x 2 = 10 get your equivalent
1
1
fraction.
+10
10
With Unlike Denominators

1x 2 = 2
5 x 2 = 10
1
1
+10
10
3
10
Remember when
denominators.
1
2
1
+8
8
8
Use the short
cut to find the
Least Common
Denominator
(LCD).
1
2x 4 = 8
1
+ 8 x 1 =8
Now find the
equivalent
fractions for
1/2 & 1/8.
Ask what do you multiply 2 by to get 8
and what do you multiply 8 by to get 8.
1x 4 =
2x 4 = 8
1x 1 =
+ 8 x 1 =8
Since you are
writing equivalent
fractions, now
multiply the top
numbers by the
same number you
did in the
bottom.
1x 4 = 4
2x 4 = 8
1x 1 =1
+ 8x 1 =8
Now multiply
across.
1x 4 = 4
2x 4 = 8
1x 1 =1
+ 8x 1 =8
5
8
new
numerators.
2
5
1
+3
15
15
Find the
common
Multiples for
5 and 3. Write
This number
denominator.
2
5 x 3 = 15
1
+ 3 x 5 =15
what you
multiply the
bottom number
by to get 15.
2x 3 =
5 x 3 = 15
1x 5 =
+ 3 x 5 =15
Multiply the
top number
by the same
number you
did in the
bottom.
2x 3 = 6
5 x 3 = 15
1x 5 =5
+ 3 x 5 =15
Multiply
across.
2x 3 = 6
5 x 3 = 15
1x 5 =5
+ 3 x 5 =15
11
15
numerators.
1x 2 = 2
6 x 2 = 12
1x 3 =3
+ 4 x 3 =12
5
12
5 x 4 = 20
6 x 4 = 24
1x 3 =3
+ 8 x 3 =24
23
24
2x 3 = 6
3x 3 = 9
1x 1 =1
+ 9x 1 =9
7
9
4 x 3 = 12
5 x 3 = 15
2 x 5 = 10
+ 3 x 5 = 15
22
15