**Largest Commonwealth Factor (FPB) and Least Common Multiple (KPK)**

1. The Greatest Common Factor (GDC) of Two Numbers

To determine the GCF of two numbers, first look for the factors of each number. Then find the common factors. After that, the largest number is selected.

Take a look at the following examples!

1. Determine the GCF from 12 and 16. Answer:

The factors of 12 are 1, 2, 3, 4, 6, 12.

The factors of 16 are 1, 2, 4, 8, 16.

The common factors of 12 and 16 are 1, 2, 4.

So the GPA of 12 and 16 is 4.

2. Determine the GCF of 8 and 24. Answer:

The factors of 8 are 1, 2, 4, 8.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

The common factors of 8 and 24 are 1, 2, 4, 8.

So, the GCF of 8 and 24 is 8.

2. Least Common Multiple (LCM) of Two Numbers

To determine the LCM of two numbers, first find the multiple of each number, then look for the common multiple. After that, the smallest number is selected.

Take a look at the examples below!

What is the LCM of 6 and 8?

Answer:

Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, ….

The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, ….

The common multiples of 6 and 8 are 24, 48, ….

So the LCM of 6 and 8 is 24.

What is the LCM of 4 and 5?

Answer:

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, ....

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ....

The common multiples of 4 and 5 are 20, 40, ....

So the LCM of 4 and 5 is 20.

3. Prime Factors of a Number

To determine the prime factors of a number can be done by using a factor tree

1. Determine the prime factors of 8!

Answer: 8 2 4 2 2 So, the prime factors of 8 = 2 × 2 × 2. 2.

4. Determining the GCF and LCM of Two Numbers by Prime Factorization What is the GCF and LCM of 6 and 8?

Answer:

Prime factors of 6 = 2 × 3.

The prime factors of 8 = 2 × 2 × 2.

a. GCF of 6 and 8 is determined by taking the same factors.

Prime factors of 6 = 2 × 3.

The prime factors of 8 = 2 × 2 × 2.

So, GCF of 6 and 8 = 2.

b. The LCM is determined by multiplying all the factors of two numbers, but the same factor is written only once.

Prime factors of 6 = 2 × 3 .

The prime factors of 8 = 2 × 2 × 2 .

So the LCM of 6 and 8 = 2 × 3 × 2 × 2 = 24.

What is the GCF and LCM of 12 and 16?

Answer: The prime factors of 12 = 2 × 2 × 3.

The prime factors of 16 = 2 × 2 × 2 × 2.

So, GCF of 12 and 16 = 2 × 2 LCM of 12 and 16 = 2 × 2 × 3 × 2 × 2 = 48.

5. FPB and KPK in Everyday Problems

a. Problems related to the KPK

1. Wati washes clothes every 3 days Erna washes clothes every 2 days. How many days do they wash on the same day?

Answer:

Wati washes clothes every 3 days

Erna washes clothes every 2 days.

LCM of 3 and 2 is 6.

So, they wash on the same day every 6 days.

2. Decorative lights in the city can be lit alternately.

The red light flashes every 3 minutes.

The blue light flashes every 4 minutes. Every how many minutes do the two lights flash together?

Answer:

The red light flashes every 3 minutes.

The blue light flashes every 4 minutes.

The LCM of 3 and 4 is 12.

So, both lights will flash together every 12 minutes.

b. Problems Related to FPB

Mr. Budi has 20 oranges and 24 apples to pack. The oranges and apples will be distributed to several children. Each child receives the same amount of oranges and the same number of apples