LCM using product notation
for 8th grade

Show the lowest common multiple of 2 numbers using product notation

To find the lowest common multiple (LCM) of two numbers, you need to find the smallest multiple that both numbers have in common. One way to do this is to use prime factorization and product notation. Here are the steps:

1. Write each number as a product of prime factors.
2. Then write the prime factors of each number, multiplying each factor by the highest power it appears in either number.

For example:
The prime factorization of one number is 2² x 3 x 5.
The prime factorization of the other number is 2 x 3² x 7.
The product notation is 2² x 3² x 5 x 7.

If required, you can simplify the product notation by multiplying the bases and their respective exponents. For example, 2² x 3² x 5 x 7 = 4 x 9 x 5 x 7 = 1260.

Here's an example of how to find the LCM of 12 and 15 using product notation:

Write each number as a product of prime factors.

• The prime factorization of 12 is 2² x 3
• The prime factorization of 15 is 3 x 5

Write the prime factors of each number in product notation, multiplying each factor by the highest power it appears in either number: 2² x 3 x 5. Note that the factor 5 appears in only one of the numbers but we still include it in the product notation.

To get the LCM as a number you can simplify the product notation by multiplying the bases and their respective exponents.

Therefore, the LCM of 12 and 15 is 2² x 3 x 5 in product notation, which is 60.

In this topic you are asked to use prime factorization to derive the lowest common multiple of 2 numbers and present your answer using product notation.