The document discusses the concept of the least common multiple (LCM). It defines the LCM as the lowest number that is a multiple of two or more numbers. It provides examples of finding the LCM of different pairs of numbers by listing their multiples and circling the first number that is common to both lists. The document also discusses how the LCM can be used to find patterns involving multiples and to add or subtract fractions by finding a common denominator.

1. Least Common Multiple
Finding the Least of the Most
Melanie Anderson

2. Least Common Multiple
• A Multiple of a number is the product of the
number and any whole number.
– Example: number x number = product (multiple)
• When you count by twos, fives or tens, you
are using multiples.
• 2: 2, 4, 6, 8, 10, 12 multiples of two
• 4: 4, 8, 12, 16, 20 multiples of four
• 5: 5, 10, 15, 20, 25 multiples of five

3. Least Common Multiple
Multiples of 6
1 x 6 = 6
2 x 6 = 12
3 x 6 = 18
4 x 6 = 24
5 x 6 = 30
6 x 6 = 36
7 x 6 = 42
Multiples of 7
1 x 7 = 7
2 x 7 = 14
3 x 7 = 21
4 x 7 = 28
5 x 7 = 35
6 x 7 = 42
The answer or product is the multiple. To help
you find the LCM make a list of the multiples of
the number then draw circle around the number
that is the same.
42 is the lowest
number that is
the same in
both list, 42 is
the LCM

4. The Least Common Multiple or the LCM is the lowest number you
get when you compare the multiples of numbers.
Ex. 1: Find the LCM of 10 and 30
10: 10, 20, 30, 40, 50
30: 30, 60, 90
So the LCM is 30 because 30 is the lowest number in the
list of multiples
Ex. 2: Find the LCM of 12 and 18
12: 12, 24, 36, 48
18: 18, 36, 54
So the LCM is 36 because 36 is the lowest number in the
list of multiples.

5. Least Common Multiple
• Ex.3 Find the LCM of 5 and 7
Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40
Multiples of 7 are 7, 14, 21, 28, 35, 42
Can you find the multiple? The lowest number
that is the same in both list.
The answer is 35. SOOOO the LCM is 35!!! Easy
right!!

6. How to use LCM?
When you are looking for a pattern?
Example: Ikisha has piano lessons every 3rd day and swim lessons
every 4th of the month. On what days will she have both piano
and swim lessons?
First look for a pattern or the LCM of both numbers.
Multiples of 3
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Multiples of 4
4, 8, 12, 16, 20, 24, 28
Circle the lowest common number
Answer: on the 12th day Ikisha will
have both piano and swim lessons.
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31

7. How to use LCM?
When you are finding a common denominator to add
or subtract fractions? This is called a LCM for least
common denominator.
Notice the denominators are not the same. Use the multiples of
4 and 2 to find the LCM.
Multiples of 4: 4, 8
Multiples of 2: 2, 4, 6 4 is the LCM or LCD ¼ + ½ =
To make the denominators the same, you multiply.
1 + 1 x 2 =2 1 + 2 = 3
4 2 x 2 =4 4 4 4
Do not
change
1/4
Now the
denominators
are alike.
Notice the
numerator and
denominator are
multiplied by 2

8. Least Common Multiple
Points to remember!!
1. A multiple is the product of two numbers.
2. List the multiples of each number to find the
common number.
3. Use LCM to find patterns.
4. Use LCM to add or subtract fractions, the
LCM becomes the LCD (the least common denominator).