Transcript 5-10 6th grade math

4-6
6th grade math
Least Common Multiple
LCM
Objective
• To find the least common multiple (LCM) of
two or three numbers.
• Why? To help you find the common
denominator when simplifying fractions. To
help you find a commonality between
numbers.
California State Standards
NS 2.4 : Determine the least multiple … of whole
numbers …
MR 3.3: Develop generalizations of the results
obtained and the strategies used and apply them
in new problem situations.
Vocabulary
• Least Common Multiple (LCM)
– The least number, other than zero, that is a multiple
of each of two or more numbers
• 4 = 12
• 3 = 12
• Multiples
– The product of a given number and another whole
number
• 2 = 2, 4, 6, 8 ,10, … ∞
How to Find the LCM
Train A travels at 10 sec
Train B travels at 6 sec
When will both first pass each
other?
Use LCM.
1. List the first 5 or so multiples
of the larger number.
2. Then start with the smaller
multiple and ask: does this
multiple share with this other
number.
3. If yes, that is you LCM. If not,
move on and continue to ask
the same question until you
find the LCM. You will always
have an LCM.
10 = 10, 20, 30, 40, 50
6=
10 = 10, 20, 30, 40, 50
6=
LCM = 30
Trains will first pass each other in
30 sec.
Another way to find LCM
Find the prime
factorization of each
number.
Write each PF aligning
common factors.
Write the product in a list,
using each common
factor once and each
other factor once.
Multiply.
(good strategy to use with
larger numbers)
84 =
72 =
84
2
42
2
21
3
7
72
2
36
2
18
2
9
3
3
PF 84 = 2, 2, 3, 7
PF 72= 2, 2, 3, 2, 3
2·2·3·7·2·3=
LCM =504
Try It!
Find LCM
1) 5, 6
2) 3, 7
1) 5 =
6 = 6, 12, 18, 24, 30,
LCM = 30
2) 3 =
7 = 7, 14, 21, 28,
LCM = 21
3) 3, 9
3) 3 =
9 = 9, 18, 17,
Try Some More!
4) 4, 14
5) 4, 6, 8
4)
4
2
14
2
2
7
PF 4 = 2, 2
PF 14 = 2, 7
LCM = 2 · 2 · 7 =
28
5)
4
2
2
8
6
2
3
PF 4 = 2, 2
PF 6 = 2,
3
PF 8 = 2, 2,
2
LCM = 2 · 2 · 3 · 2 =
24
2
4
2
2
Objective Review
• To find the least
common multiple (LCM)
of two or three
numbers.
Why? You can now find the
common denominator
when simplifying fractions.
You can now find a
commonality between
numbers.
Independent Practice
• Complete problems 712
• Copy original problem
first.
• Show all work!
• If time, complete Mixed
Review: 13-19
• If still more time, work
on Accelerated Math.