4. Problem A
Elvira is going to prepare bouquets of
roses and bouquets of daisies. She has
36 roses and 24 daisies. What is the
greatest number of each flower that
she can use in a bouquet if bouquets
have the same number of flowers.
• What is Elvira going to do with the
flowers?
• How many roses does she have?
• How many daisies?
5. Problem B
Divina is going to prepare bouquets of
roses with 5 roses to a bouquet and
bouquets of daisies with 6 daisies to a
bouquet. What will be the smallest number
of roses and daisies that she will need for
her bouquets?
• What is Divina planning to do?
• How many roses will she need to prepare a
bouquet of roses?
• How many daisies does she need to prepare
a bouquet of daisies?
6. Problem A: Solution 1
Finding the Greatest Common Factor (GCF)
by listing the factors of 36 and 24.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18,
and 36.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12,
and 24
Common Factors: 1, 2, 3, 4, , and 12
Greatest Common Factor: 12
7. Solution 2: Finding the Greatest Common
Factor (GCF) of 36 and 24 by prime
factorization.
36 = 2 × 2 × 3 × 3
24 = 2 × 2 × 2 × 3
Common Prime Factors: 2 × 2 × 3
GCF: 12
Solution 3: Finding the GCF of 24 and 3 by
continuous division.
GCF: 2 × 2 × 3
2 24 36
2 12 18
3 6 9
2 3
8. Problem B: Solution
1
Finding the Least Common Multiple (LCM)
by listing some multiples of 5 and 6.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35,
40, 45, 50, 55, 60, …
Multiples of 6: 6, 12, 18, 24, 30, 36, 42,
48, 54, 60, …
Common Multiples of 5 and 6: 30,
60, …
Least Common Multiples (LCM): 30
9. Solution 2: Finding the Least Common
Multiple (LCM) of 5 and 6 by prime
factorization.
5 = 1 × 5
6 = 2 × 3
LCM = 1 × 2 × 5 × 3 = 30
Solution 3: Finding the Least Common
Multiple (LCM) of 5 and 6 by continuous
division.
LCM: 2 × 5 × 3 = 30
2 5 6
3 5 3
5 5 1
1 1
10. For Problem A
• We used the 4-step plan in solving
problem in solving GCF and LCM of
two numbers. Understand, Plan,
Solve, and Check and Look Back.
• We solved for the answer by listing
method, prime factorization, and
continuous division.
11. Cherry baked 48 pieces of butler cookies and
60 chocolate cookies. If she will put them
separately in boxes, what is the most
number of cookies the boxes will contain if
theses are of the same number?
How will you solve for the answer to the
problem?
You can use the 4-step plan
in solving for the answer.
12. Understand:
What does the problem
ask for?
The greatest number of cookies
that a box will contain.
What facts are given?
48 butter cookies, 60 chocolate
cookies
Plan:
How will you solve the
problem?
By listing the factors
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and
48
60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20,
30, and 60.
GCF: 12
By Prime Factorization
48 = 2 × 2 × 2 × 2 × 3
60 = 2 × 2 × 3 × 5
GCF: 2 × 2 × 3 = 12
Check and Look Back:
13. Solve the following problems:
1. Aira baked 60 cupcakes and 48
cookies. If she is going to pack them in
boxes of cupcakes and boxes of
cookies, what is the most number of
each item will the boxes contain if
these are of the same number
2. Aling Maring is going to sell suman in
bundles. What is the least number of
suman that she could sell in bundles of
3 and 5?
14. Read each problem and answer the questions
that follow. Write your answers in your
notebook.
1. There are 16 boys and 24 girls. If they will
be grouped separately in teams with the
same number, what is the biggest
number of children in a group?
a. What is asked for in the problem?
______________
b. What facts are given? ___________
c. How will you solve the problem?
___________
15. 2. Mang Andoy is going to put eggs in trays
of 6 eggs and 12 eggs. What is the
smallest number of eggs that Mang
Andoy can put using the trays?
a. How will you solved the problem?
_____________
b. What is the answer to the problem?
__________________
Read each problem and answer the
questions that follow. Write your
answers in your notebook.
16. Read and solve each problem.
Write the solution in your
notebook.
1. Mrs. Lim has 56 cups and 64 glasses.
If she will put them in trays of cups and
trays of glasses with the same number,
what is the biggest number of cups or
glasses that a tray will contain?
2. A factory is to pack pencils in boxes of
8 and 10 pieces. What is the smallest
number of pencils that can be packed
using the boxes?
17. How do we solve problem solving
involving GCF and LCM of two
given numbers?
• We use the 4-step plan in solving
problems involving GCF and LCM of two
given numbers. Understand, Plan, Solve,
and Check and look Back.
• We solve for the answer by listing
method, prime factorization, and
continuous division.
18. Challenge yourself by solving these
problems. Write your answers in your
notebook.
1. What is the smallest number of avocados that
can be placed in baskets with 50 and 75 pieces?
2. What is the largest number of pechay and
cabbage plants that can be planted in rows of
equal number if there are 60 pechay and 80
cabbage plants?
3. Mary has some chocolates. If she shares them
equally among 4 friends or 5 friends, there are
always 2 extra chocolates left. What is the
possible number of chocolates Mary could have?
4. Biscuits are sold in packs of 10, 15, and 20
19. Read and solve each problem.
Write you answers on your
answer sheet.
1. Mr. Roldan’s class is composed of
28 boys and 35 girls. It he is going to
make groups of boys and group of
girls for the activities, what is the
biggest number of children in the
group if they are of the same number?
2. Darie is going to pack puto in boxes
of 6 and 12 pieces. What is the
smallest number of puto that she can
20. Provide more practice on finding GCF and LCM of
two numbers. Then, give problems similar to
those given in the lesson.
Read and solve each problem. Write the
answers in your notebook.
1. Oranges are sold in boxes of 6, 8, 10, and
12. How can Mario buy 60 oranges?
2. A bell rings every 15 seconds. A horn
blows every 30 seconds. If Kathy heard the
two sounds at 9:00 a.m., at what time will
she hear the sounds together again?
