# -c03 write prime factorization of the LCM of A and B

• MHB
• karush
Otherwise, it is the product of the highest powers of each prime factor present in A and B. In summary, the least common multiple of A and B is $2 \cdot 3^2 \cdot 5 \cdot 7^3 \cdot 11^3 \cdot 13^2$, and the greatest common factor is $3^2 \cdot 5 \cdot 7^2 \cdot 11^2$.
karush
Gold Member
MHB
Build the least common multiple of A and B
a. write the prime factorization of the least common multiple of A and B.
$A=2\cdot 3^2\cdot 5\cdot 7^3\cdot 11^3\cdot 13^2$
$B= 3^2 \cdot 5 \cdot 7^2 \cdot 11^2$
$\dfrac{2\cdot \cancel{3^2}\cdot \cancel{5\cdot 7^2} 7\cdot \cancel{11^2} 11\cdot 13^2} {\cancel{3^2} \cdot 5 \cancel{\cdot 7^2} \cdot \cancel{11^2}} =2\cdot 7\cdot 11\cdot 13^2=26026$

not sure if I went the right direction on this how do we get the prime factorization

The LCM would be …

$2 \cdot 3^2 \cdot 5 \cdot 7^3 \cdot 11^3 \cdot 13^2$

The GCF would be …

$3^2 \cdot 5 \cdot 7^2 \cdot 11^2$

so its not A and B together? altho B is subset of A

LCM is A times B (together) only if A and B are relatively prime

## 1. What is the LCM of A and B?

The LCM (Least Common Multiple) of A and B is the smallest positive integer that is divisible by both A and B.

## 2. How is the LCM of A and B calculated?

The LCM of A and B can be calculated by finding the prime factorization of both A and B, and then multiplying the highest power of each prime factor together.

## 3. What does the "-c03 write prime factorization" part mean?

The "-c03" refers to a specific method or format for writing the prime factorization. It may vary depending on the context or specific instructions given.

## 4. Can the LCM of A and B be written in different ways?

Yes, the LCM of A and B can be written in different ways depending on how the prime factorization is written. For example, the LCM of 12 and 18 can be written as 36 or as 2^2 * 3^2.

## 5. Why is it important to find the LCM of A and B?

Finding the LCM of A and B is important in many mathematical applications, such as simplifying fractions, finding common denominators, and solving problems involving multiple quantities or rates. It is also a fundamental concept in number theory and can help with understanding the relationships between numbers.

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