Build the least common multiple of A and B using the example/method in module 8 on page 59860. Then write the prime factorization of the least common multiple of A and B. A = 22.33.52.7.11³.13 B= 22.3.53.72 11². 133 Submit Question
Build the least common multiple of A and B using the example/method in module 8 on page 59860. Then write the prime factorization of the least common multiple of A and B. A = 22.33.52.7.11³.13 B= 22.3.53.72 11². 133 Submit Question
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**How to Find the Least Common Multiple (LCM) of Two Numbers**
To find the Least Common Multiple (LCM) of two numbers, follow the method outlined in your textbook (module 8 on page 59 & 60). Here, we’ll walk you through the process using an example.
**Problem:**
Given the prime factorizations of two numbers:
\[ A = 2^2 \cdot 3^3 \cdot 5^2 \cdot 7 \cdot 11^3 \cdot 13 \]
\[ B = 2^2 \cdot 3 \cdot 5^3 \cdot 7^2 \cdot 11^2 \cdot 13^3 \]
We need to find the prime factorization of the LCM of \( A \) and \( B \).
**Solution:**
The LCM is found by taking the highest power of each prime that appears in the factorization of the given numbers.
- **Step 1: List all the unique primes in the prime factorizations of A and B:**
\[ 2, 3, 5, 7, 11, 13 \]
- **Step 2: Select the highest power of each prime:**
- For \( 2 \): The highest power is \( 2^2 \).
- For \( 3 \): The highest power is \( 3^3 \).
- For \( 5 \): The highest power is \( 5^3 \).
- For \( 7 \): The highest power is \( 7^2 \).
- For \( 11 \): The highest power is \( 11^3 \).
- For \( 13 \): The highest power is \( 13^3 \).
- **Step 3: Form the LCM using these selected powers:**
\[
\text{LCM} = 2^2 \cdot 3^3 \cdot 5^3 \cdot 7^2 \cdot 11^3 \cdot 13^3
\]
**Note:**
When entering your answer in the designated field, use the format shown in the problem statement, ensuring to use the correct exponents for each prime factor.
**Submit your solution in the provided field and click "Submit Question](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ee3c1cf-5502-4aa3-81a2-22fca9c39339%2F10ba4e88-50e4-4182-940c-e92c28f228e1%2Fdevzf5a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**How to Find the Least Common Multiple (LCM) of Two Numbers**
To find the Least Common Multiple (LCM) of two numbers, follow the method outlined in your textbook (module 8 on page 59 & 60). Here, we’ll walk you through the process using an example.
**Problem:**
Given the prime factorizations of two numbers:
\[ A = 2^2 \cdot 3^3 \cdot 5^2 \cdot 7 \cdot 11^3 \cdot 13 \]
\[ B = 2^2 \cdot 3 \cdot 5^3 \cdot 7^2 \cdot 11^2 \cdot 13^3 \]
We need to find the prime factorization of the LCM of \( A \) and \( B \).
**Solution:**
The LCM is found by taking the highest power of each prime that appears in the factorization of the given numbers.
- **Step 1: List all the unique primes in the prime factorizations of A and B:**
\[ 2, 3, 5, 7, 11, 13 \]
- **Step 2: Select the highest power of each prime:**
- For \( 2 \): The highest power is \( 2^2 \).
- For \( 3 \): The highest power is \( 3^3 \).
- For \( 5 \): The highest power is \( 5^3 \).
- For \( 7 \): The highest power is \( 7^2 \).
- For \( 11 \): The highest power is \( 11^3 \).
- For \( 13 \): The highest power is \( 13^3 \).
- **Step 3: Form the LCM using these selected powers:**
\[
\text{LCM} = 2^2 \cdot 3^3 \cdot 5^3 \cdot 7^2 \cdot 11^3 \cdot 13^3
\]
**Note:**
When entering your answer in the designated field, use the format shown in the problem statement, ensuring to use the correct exponents for each prime factor.
**Submit your solution in the provided field and click "Submit Question
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