Least Common Multiple - Rutherford County Schools

Least Common Multiple
Chapter 5 Lesson 1
EQ: How do we find the LCM?
Multiples


A multiple is formed by multiplying a
given number by the counting numbers.
The counting numbers are 1, 2, 3, 4, 5,
6, etc.
Example: List the multiples of 4:






4x1=4
4x2=8
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
4 x 6 = 24
Counting Numbers
So, the multiples of 4
are 4, 8, 12, 16, 20, 24,
28, etc.
What are the first five multiples of
13?
13 x 1 =13
13 x 2 = 26
13 x 3 = 39
13 x 4 = 52
13 x 5 = 65
13, 26, 39, 52, 65
Find the Missing Multiples
 6,
30
24 ____
12, 18, ____,
3
 ___,
15 ____,
18 21
6, 9, 12, ____,
12
 ___,
72
24, 36, 48, 60, ____
Least Common Multiple (LCM)

The least common multiple is the smallest
number that is common between two lists of
multiples.
EXAMPLE:
Find the LCM of 12 and 18
The multiples of 12:
The multiples of 18:
•12 x 1 = 12
•18 x 1 = 18
•12 x 2 =24
•18 x 2 = 36
•12 x 3 = 36
•18 x 3 = 54
•12 x 4 = 48
•18 x 4 = 72
•12 x 5 =60
•18 x 5 = 90
12, 24, 36, 48, 60
18, 36, 54, 72, 90
The first number you see in both lists
is 36.
The least common multiple of 12
and 18 is 36.
Example 2:
Find the LCM of 9 and 10
9, 18, 27, 36, 45, 54, 63, 72 81, 90, 99
10, 20, 30, 40, 50, 60, 70, 80 90, 100, 110
If you don’t see a common multiple, make
each list go further.
The LCM of 9 and 10 is 90
Example 3:
Find the LCM of 4 and 12
4, 8, 12, 16
12, 24, 36
Using Prime Factorization to find
the LCM
• Make factor trees for each number. Write the
prime factorization in exponent form.
•Identify all of the prime numbers among the prime
factorizations. Every prime number will be used.
• When the same prime number occurs in more
than one prime factorization, select the prime that
there’s more of (for example, 25 beats 22.)
• Multiply your prime numbers to get the LCM.
Example: Find the LCM of 88 and
102
88
102
2 x 44
2 x 51
2 x 22
2 x 11
88 = 23 x 11
102 = 2 x 3 x 17
LCM: 23 x 3 x 11 x 17 = 4,488
3 x 17
We have to use every prime number. The
numbers we will use are 2, 3, 11, and 17.
We have 2 in both places. Select the “bigger”
one. 23 beats regular 2.
Homework Time