Essential Question: How do you find the greatest common factor and least common multiple of monomials?

Before we start…
You have 12𝑥𝑦 apples and your friend has 6𝑥 apples. How many apples do you have in common?

What is a
?
Any whole number that can be divided exactly into another number.
1, 2, 3, and 6 are factors of 6.

What is a
?
A whole number that is a factor of two or more nonzero whole numbers.
3 is a common factor of 3, 6, 9 and 12.

•
The greatest common factor (GCF) is the greatest of the common factors.
– It’s the highest number factor that appears in each number’s factor list.
•
12 has the factors: 1, 2, 3, 4, 6 and 12.
•
16 has the factors: 1, 2, 4, 8 and 16.
–
The GCF of 12 and 16 would be 4 .

•
Write the prime factorization of each number.
•
Circle the smallest power of each factor.
•
Find the product of your circled factors. Your product is the GCF .

Find the greatest common factor of 12𝑎 3
9𝑎 2
.
and

Find the greatest common factor of 6𝑥𝑦 and
4𝑥𝑦 2
.

Find the greatest common factor of 15𝑦 and
9𝑥 2 𝑦 2
.

Find the greatest common factor of 5𝑥𝑦 3
10𝑥 2 𝑦 2
.
and

Find the greatest common factor of 6𝑥 and 18𝑥 .

What is a
?
The product of the number and any nonzero whole number.
A common multiple is a multiple that is shared by two or more numbers.

What is a
?
•
A least common multiple (LCM) is the least common multiples of two or more whole numbers.
– It’s the smallest answer that two numbers share .

•
Write the prime factorization of each number.
•
Circle the greatest power of each prime factor.
•
Find the product of the circled factors. This is your LCM.

Find the LCM of 6𝑥 2 𝑦 and 9𝑥 4 𝑧 .

Find the LCM of 8𝑥 3 and 20𝑥 7
.

Find the LCM of 4𝑎𝑏 2 and 10𝑎 2 𝑏 .

Find the LCM of 6𝑚 3 𝑛𝑝 2 and 8𝑚𝑝 3
.

Find the LCM of 4𝑥 3 𝑦 3 and 18𝑥𝑦 5
.

Find the LCM of 24𝑐 2 𝑑 3
, 30𝑐 3 𝑑 2 and 60𝑐 2 𝑑 6
.

How do you find the greatest common factor and least common multiple of monomials?

Find the LCM of 9𝑦 4 and 12𝑦