Lesson Plan of LCM Using Prime Factorization / Division Method Mathematics Grade V
Lesson Plan of LCM Using Prime Factorization / Division Method
Mathematics Grade V
Students’ Learning Outcomes
·
Find LCM of four numbers, up
to 2 digits, using prime factorization method.
·
Find LCM of four numbers, up
to 2 digits, using division method.
Information for Teacher
·
Since the students have done
both factorization and division method for finding H CF, so they won’t find this
difficult.
·
First go with three numbers
questions and explain both methods, then individual or group work and then
discuss on four numbers questions.
·
When any number is used to
multiply with the set of natural numbers {1, 2, 3, ……}, the product of that
number with each of the natural numbers is called multiples of that number,
e.g. the multiples of three are : 3(1), 3(2(, 3(3), 3(4(, …. Which are
respectively equal to 3, 6, 9, 12……..
·
The number/multiple among the
common multiples of two or more numbers is called the least common multiple.
·
Least common multiple is
abbreviated as ‘LCM’.
·
Find LCM of two or more
numbers through multiples.
·
In this method we find few
multiples of all given numbers, then write the common multiples separately and
the smallest of these common multiples is called LCM.
·
Find LCM of 6, 8 and 12 by
finding multiples.
·
Find LCM of two or more
numbers through prime factorization.
·
In prime factorization method
the product of common and uncommon factors is called LCM.
·
In this method, first write
prime factorization of each given number, then in each factorization, the
factors repeating, write them in exponential form.
·
Separate all highest power
factors from all factorizations.
·
Now the product of all
factors is called LCM.
·
Find LCM of 72, 24, 96 and 12
by using prime factorization.
·
LCM of the given numbers = in
all factorizations, product of all such prime factors which having highest
exponent.
·
Instead of writing factors in
exponential form, you can identify all the common factors after factorization
of each number, and then product of all common and uncommon factors is called
LCM.
·
To find LCM while writing the
common factors, keep in mind that it is not necessary that common factors are
common in all given numbers, if they are common in at least two of given
numbers then these are also consider in common numbers.
LCM of given numbers =
product of common factors (including factors common in at least two numbers)
and uncommon factors.
= 2 x 2 x 2 x 3 x 2 x 2 x 3
LCM = 288
·
Find the LCM of two or more
numbers using division method.
·
To find LCM of two or more
numbers using division method, we continue the division process until below all
numbers we have 1’s as quotient.
·
The divisors may be prime and
composite, but try to divide with smallest number.
·
In this method the product of
divisors of the numbers is called LCM.
·
Like finding H CF by using
division method (Ladder method) it is not necessary that all the numbers will
divide with one divisor. I.e. the number which is not divisible by that
divisor, then simply write that number down.
·
Find LCM of 72, 24, 96 and 12
using division method.
·
During teaching the lesson,
teacher should concern with text book, when and where necessary in all steps.
Material / Resources
Board, marker/chalk, duster, text book
Worm up activity
·
Divide the students in pairs.
·
Inform students that you can
discuss with each other about factors of numbers and prime factorization for
one minute.
·
They will need to select
which student will begin first.
·
Provide students with the
three or four questions to help in their discussion.
·
For discussion in pairs,
allocate time two minute.
·
At one minute, instruct
students to switch. At this point, the other partner begins talking.
·
It is OK for the second
student to repeat some of the things the first student said.
·
However, they are encouraged
to try and think of new information to share.
Two minute sample questions:
o
What are factors?
o
Can you tell two things about factors?
o
What are prime or composite factors?
o
How would you find the factors of a number?
o
What is meant by factorization?
o
What is prime factorization?
Development
Activity 1
·
Inform the students that the
numbers divide any number exactly is called factors of this number. E.g. all
possible factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
·
In these factors 2, 3, 5 are
prime factors while 6, 10, 15, 30 are composite factors.
·
Now tell the students that to
write any number as a product of its factors is called factorization. E.g.
number 30 can be expressed as a product of its factors in different ways. I.e.
following are the factorizations of 30, 30 = 1 x 30 or = 2 x 15 or =3 x 10 or =
5 x 6 or = 2 x 3 x 5.
·
Similarly to express any
number as a product of its prime factors is called prime factorization. As
according to above example, prime factorization of 30 = 2 x 3 x 5.
·
All possible factors of 18 are
1, 2, 3, 6, 9, and 18.
·
In these factors 2, 3 are
prime factors while, 6, 9, 18 are composite factors.
·
Number 18 can be expressed as
a product of its factors in different ways. I.e. following is the factorization
of 18, 18 = 1 x 18 or =2 x 9 or = 3 x 6.
·
Similarly prime factorization
of 18 = 2 x 3 x 3
·
A prime factorization of a
number can be written in the exponential form.
E.g. 18 = 2 x 3 x 3 = 2 x 32
36 = 2 x 2 x 3 x 3 = 22
x 32
Activity 2
·
Are you ready for something
new but as interesting as H CF was.
· OK tell what do we mean by
the word product?
·
Write 3, 4, and 6 on board
and tell the students we are interested in the smallest number that is
divisible by 3, 4 and 6.
·
If we should find the product
of all three numbers i.e. we multiply 3 x 4 x 6 = 72. It seems logical that 72
should be easily divisible by 3, 4 and 6 since 72 is the product of these
numbers.
·
Ask the students, “Is 72 the
smallest number that is divisible by 3, 4 and 6?”
·
After collecting response
from students tells that the answer is “no”, since 36, which is one-half of 72,
is also divisible by 3, 4 and 6.
·
Conclude that such a smallest
number that is divisible by all given numbers is called LCM.
Activity 3
·
Write on the board 42, 96 and
24 or any other question from text book.
·
Ask the students to write the
given numbers as product of prime factors. E.g. 2 x 2 x 3 etc.
·
Now write in exponential
form, the numbers which are repeating again and again in each factorization.
·
After few minutes, teacher
does them on the board as done in the example given in “information for
teacher”.
·
Now ask them to write the
highest power factors as product. E.g. 25 x 32.
·
Give few minutes to try, and
then ask them to find answer. Thumb up who does it.
·
Now do it on the board and
explain according to the method given in “information for teacher”.
·
Conclude that we find LCM of
these numbers using prime factorization.
·
Repeat this concept with the
help of another example.
·
If students feel difficult to
write in exponential form and finding LCM, then ask them to write all the common
factors and uncommon factors as product and then find LCM.
·
Now tell the students, how to
solve the question according to this method.
·
For practice give students in
groups, one or two-digit three numbers than four numbers questions and ask them
to find LCM using prime factorization.
Activity 4
·
Ask students, do you remember
the short cuts to check whether the number is divisible by 2, 3, and 5 or 10?
·
After taking their answer,
tell the divisibility test rules to all.
·
Divisible by 2 if the last
digit (ones digit) is 0, 2, 4, 6 or 8 example 12345.
·
Divisible by 5 if the sum of
digits in the number is divisible by 3. Example 12345.
·
Divisible by 5 if the last
digit (ones digit) is 0 or 5 example 2345.
·
Divisible by 10 if the last
digit (ones digit) is ‘0’ example 99990
·
Tell them that this will help
them while doing LCM with division method.
Activity 5
·
Write 3, 4 and 6 on board and
solve with the help of students.
·
Now start dividing each
number by the smallest number like 3, write their answer (quotient) below these
numbers.
·
If any of the numbers is not
divisible by 3, simply write that number down.
·
Again start dividing by any
smallest number like 2 and then, if any of the numbers is not divisible by it,
write that number down.
·
Continues this process until
in the last line, below each number we have all 1’s as quotient.
·
Now by multiplying all the
divisors we get LCM.
·
Conclude that we have found
the LCM of these numbers by division method.
·
Repeat this concept with the
help of another example.
·
For practice give students in
groups, one or two-digit three numbers than four numbers questions and ask them
to find LCM using division method.
Activity 6
·
Assign one question to each
student and ask to find LCM by using both methods.
·
Allocate time.
·
Ask students to check each
other work and correct the mistakes.
·
Guide the students in
question solving.
Sum up / Conclusion
·
Least common multiple is
abbreviated as ‘LCM’.
·
Recap the method of finding
LCM using prime factorization.
·
Recap the following method of
finding LCM using division.
·
We write down the numbers
horizontally.
·
We draw a vertical line to
the left of the numbers and draw horizontal line under the numbers.
·
We than look for the smallest
number that can divide any of the numbers exactly.(try to select the prime divisor)
·
If any of the numbers is
divisible by divisor, writing down the answer of that division below line.
Similarly if any of the numbers is not divisible by divisor, write that number
down below the line.
·
Then we draw another
horizontal line and repeat this process.
·
When you get all 1’s as
quotient in a horizontal line, then multiply all the divisors that are
vertical, and the product called LCM.
·
Solve question on board
according to both methods.
Assessment
·
Find LCM of 48, 24, 16 and 72
by using prime factorization method.
·
Find LCM of 30, 18, 68, 8 by
using division method.
Follow up
Questions
|
By using prime factorization
|
By using division
|
·
Draw the above said table on
board, write questions and ask students to find LCM by both methods.
Comments
Post a Comment