Least
Common
Multiple
Why?
Three
Quick
Examples


The
Answer
It gets
larger.
“Here are two numbers. Find their LCM.”
Find the smallest number
such that each of the two given numbers
divides evenly (no remainder) into that
number. That’s the LCM.
It will be at least as big as the larger of the
two numbers in the question.
LCM is used for finding the Common Denominator in adding fractions.
LCM is used to “Clear The Fractions” and make equations easier to solve.
The LCM of 14 and 28 …
is 28.
The LCM of 10 and 21 …
is 210.
The LCM of 10 and 15 …
is 30.
How?
❶ Shortcut
❷ Sometimes you
just look at it and
you know instantly.
❸ Sometimes you
count up by
multiples of the
larger number.
❹ Sometimes you
have to make prime
factor trees and a
table.
LCM.docx
The
Question
12/15/2011 1:54 PM
Sometimes the smaller number divides
evenly into the larger number.
Sometimes the LCM is the product of the
two numbers. This happens when they have
no common factors.
Sometimes the LCM is higher than the higher
number, but lower than the product.
Here are several ways.
Sometimes you use one way. Sometimes you use another way.
Have a full toolbox. It will save time and make things easier for you.
If the smaller number
Q: The LCM of 15 and 180 is …?
divides into the larger
Think: 180 div by 15 = 12 r 0
number, the larger
A: The LCM is 180.
number is your answer.
(d) The LCM of 2 and 112 is…
Try these.
(e) The LCM of 4 and 5 is…
(a) The LCM of 5 and 3 is…
(f) The LCM of 6 and 4 is…
(b) The LCM of 6 and 3 is…
Answers:
(c) The LCM of 6 and 9 is…
(a) 15 (b) 6 (c) 18 (d) 112 (e) 20 (f) 12
The LCM of 24 and 40 is what?
 40 is the larger number.
 so think: 40, 80, 120, 160, 200, 240, …
 Stop when you find one where 24 divides into it evenly.
 24 into 40? No, has a remainder. 24 into 80? No.
 24 into 120 = 5 remainder 0. Stop. The LCM of 24 and 40 is 120.
The LCM of 60 and 126 is what?
1) Do factor trees.
2) One column for
each prime factor.
3) LCM = multiply all
the columns.
60
= 2 ∙ 2 ∙ 3 ∙
5
126 = 2 ∙
∙ 3 ∙ 3 ∙
7
LCM = 2 ∙ 2 ∙ 3 ∙ 3 ∙ 5 ∙ 7
The LCM of 60 and 126 is 1260.
More LCM stuff on the other side →→→
Least
Common
Multiple
TI-84 can
do LCM
The
Answer
It gets
larger.
“Here are two numbers. Find their LCM.”
Find the smallest number
such that each of the two given numbers
divides evenly (no remainder) into that
number. That’s the LCM.
It will be at least as big as the larger of the
two numbers in the question.
Type the first number
then , comma
then the second number
then ENTER.
Press MATH.
Press →to the NUM submenu.
Press 8 for lcm(
What if you want the LCM of
three or more numbers?
1. Find the LCM of two of the
numbers.
2. Find the LCM of that answer
and the third number.
3. Etc. if there’s more numbers
in the list.
The big chart with prime
factorizations can be extended
to do LCM and GCF of three or
more numbers at a time.
LCM.docx
The
Question
12/15/2011 1:54 PM
Example:
Find the LCM of 60, 126, and 93.
1. The LCM of 60 and 126 is
1260 (we did this on the front
side).
2. The LCM of 1260 and 93 is
39060.
60
126
93
LCM
GCF
= 2 ∙ 2 ∙ 3 ∙
5
= 2 ∙
∙ 3 ∙ 3 ∙
7
=
3 ∙
∙
= 2 ∙ 2 ∙ 3 ∙ 3 ∙ 5 ∙ 7 ∙
=
3
31
31
More LCM stuff on the other side →→→