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

```Fraction XI
With Unlike Denominators
By Monica Yuskaitis
Common Multiple

A number that is a multiple
of two or more numbers.
Some multiples of 3 & 4
12, 24, 36, 48,
Least Common Multiple

The smallest common multiple
of a set of two or more
numbers.
4 = 4, 8, 12, 16, 20, 24, 28
5 = 5, 10, 15, 20, 25, 30
Mixed Numbers

Mixed numbers are whole
numbers and fractions together.
1
3 2
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 2
1
+ 1 8
2 will divide evenly into 8,
so 8 is your LCD or LCM.
Numbers With Unlike
Denominators

Find the multiples of each
denominator.
1
3
4 = 4, 8, 12, 16, 20, 30
1
1
+ 10 = 10, 20, 30, 40, 50
Unlike Denominators

Compare the lists of multiples.
Circle the common multiples
between the two lists.
1
3
4 = 4, 8, 12, 16, 20, 24
1
1
+ 10 = 10, 20, 30, 40, 50
Unlike Denominators
Use the least common
multiple as the denominator.

1
3
4 = 4, 8, 12, 16, 20, 24
1
1
+ 10 = 10, 20, 30, 40, 50
Unlike Denominators
This number is also called
the least common denominator.

1
3
4 = 4, 8, 12, 16, 20, 24
1
1
+ 10 = 10, 20, 30, 40, 50
Unlike Denominators

Find the equivalent fractions for 1/4
& 1/10 with 20 as the denominator.
1
3
4 x 5 =20
1
1
+ 10
20
you multiply 4 by
to get 20.
Unlike Denominators

Find the equivalent fractions for 1/4
& 1/10 with 20 as the denominator.
1
x
5
=
3
4 x 5 =20
1
1
+ 10
20
That’s right 5. Since
you are looking for
the equivalent fraction
you know the top
number must also be
multiplied by 5.
Unlike Denominators

Find the equivalent fractions for 1/4
& 1/10 with 20 as the denominator.
1
5
x
5
=
3
4 x 5 =20
1
1
+ 10
20
To find the top number
just multiply 1 x 5 to
fraction.
Unlike Denominators

Find the equivalent fractions for 1/4
& 1/10 with 20 as the denominator.
1
5
x
5
=
3
4 x 5 =20
1
1
+ 10x 2 =20
multiply the 10 by
to get 20.
Unlike Denominators

Find the equivalent fractions for 1/4
& 1/10 with 20 as the denominator.
1
5
x
5
=
3
4 x 5 =20
1
2
x
2
=
1
+ 10x 2 =20
That’s right 2. Since yo
are looking for the
equivalent fraction you
know the top number
must also be multiplied
by 2.
Unlike Denominators

1
5
x
5
=
3
4 x 5 =20
1x 2 = 2
+1 10x 2 =20
7
20
Remember! We
denominators.
Unlike Denominators

1
5
x
5
=
3
4 x 5 =20
1x 2 = 2
+1 10x 2 =20
7
4 20
1
10 3
1
+3 6
6
6
Use the short
cut to find the
Least Common
Denominator
(LCD).
1
10 3 x 2 = 6
1
3
+ 6 x 1 =6
Now find the
equivalent
fractions for
1/3 & 1/6.
Ask what do you multiply 3 by to get 6
and what do you multiply 6 by to get 6.
1
x
2
=
10
3x 2 = 6
1
x
1
=
+ 3 6 x 1 =6
Since you are
writing equivalent
fractions, now
multiply the top
numbers by the
same number you
did in the
bottom.
1
2
x
2
=
10
3x 2 = 6
1
1
x
1
=
3
+ 6x 1 =6
Now multiply
across.
1
2
x
2
=
10 3 x 2 = 6
1
1
x
1
=
3
+ 6x 1 =6
3
6
new
numerators.
1
2
x
2
=
10 3 x 2 = 6
1
1
x
1
=
3
+ 6x 1 =6
3
13
6
whole
numbers.
3
3
1
÷
13
13
=
6 ÷3
2
4
11
5
1
2
+ 3
15
15
Find the
common
multiples for
5 and 3. Write
this number
denominator.
4
11 5 x 3 = 15
1
+ 2 3 x 5 =15
what you
multiply the
bottom number
by to get 15.
4
x
3
=
11
5 x 3 = 15
1
x
5
=
+ 2 3 x 5 =15
Multiply the
top number
by the same
number you
did in the
bottom.
4
12
x
3
=
11
5 x 3 = 15
1x 5 =5
+ 2 3 x 5 =15
Multiply
across.
4
12
x
3
=
11
5 x 3 = 15
1
5
x
5
=
2
+ 3 x 5 =15
17
15
numerators.
to a Mixed Number
4
12
x
3
=
11
5 x 3 = 15
1
5
x
5
=
2
+ 3 x 5 =15
17
15
2
1 15
15) 17
15
2
Numbers
1
4
12
x
3
=
11
5 x 3 = 15
1
5
x
5
=
2
+ 3 x 5 =15
17
14
15
2
1 15
15) 17
15
2
1
4
12
x
3
=
11
5 x 3 = 15
1
5
x
5
=
2
+ 3 x 5 =15
17
14 2
15
15
2
1 15
15) 17
15
2
1
4
12
x
3
=
11
5 x 3 = 15
1
5
x
5
=
2
+ 3 x 5 =15
17
14 2
15
15
2
1 15
15) 17
15
2
1
24 5 x 4 = 20
6 x 4 = 24
5
15
x
3
=
3
+ 8 x 3 =24
11
35
28
24 24
11
1 24
24) 35
24
11
```