Find the greatest common factor and the least common multiple of A and B. Write your answers as a product of powers of primes in increasing order. A= 3³.53.72.11³.13 B=2-3³-133 GCF (A,B) = LCM(A,B)
Find the greatest common factor and the least common multiple of A and B. Write your answers as a product of powers of primes in increasing order. A= 3³.53.72.11³.13 B=2-3³-133 GCF (A,B) = LCM(A,B)
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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![**Greatest Common Factor and Least Common Multiple Problem**
Please solve the following problem by finding the greatest common factor (GCF) and the least common multiple (LCM) of the numbers \(A\) and \(B\). Write your answers as a product of powers of primes in increasing order.
Given:
\[ A = 3^3 \cdot 5^3 \cdot 7^2 \cdot 11^3 \cdot 13 \]
\[ B = 2 \cdot 3^3 \cdot 13^3 \]
**Tasks:**
1. Determine the greatest common factor (GCF) of \(A\) and \(B\).
2. Determine the least common multiple (LCM) of \(A\) and \(B\).
### Input Fields:
- **GCF(A,B)**: [ _______ ]
- **LCM(A,B)**: [ _______ ]
[Submit Question]
### Explanation of Terms:
- **Greatest Common Factor (GCF)**: The largest positive integer that divides each of the given numbers without a remainder.
- **Least Common Multiple (LCM)**: The smallest positive integer that is divisible by each of the given numbers.
Analyzing the prime factorization provided:
- The prime factors for \(A\) are \(3^3\), \(5^3\), \(7^2\), \(11^3\), and \(13\).
- The prime factors for \(B\) are \(2\), \(3^3\), and \(13^3\).
To find the GCF and LCM:
- **GCF**: Take the lowest power of each prime common to both numbers.
- **LCM**: Take the highest power of each prime that appears in either number.
Please input the correct GCF and LCM values in their respective fields and click "Submit Question" to check your answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ee3c1cf-5502-4aa3-81a2-22fca9c39339%2F69adbaec-8709-4958-af09-7da778c5094a%2Faozvj8b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Greatest Common Factor and Least Common Multiple Problem**
Please solve the following problem by finding the greatest common factor (GCF) and the least common multiple (LCM) of the numbers \(A\) and \(B\). Write your answers as a product of powers of primes in increasing order.
Given:
\[ A = 3^3 \cdot 5^3 \cdot 7^2 \cdot 11^3 \cdot 13 \]
\[ B = 2 \cdot 3^3 \cdot 13^3 \]
**Tasks:**
1. Determine the greatest common factor (GCF) of \(A\) and \(B\).
2. Determine the least common multiple (LCM) of \(A\) and \(B\).
### Input Fields:
- **GCF(A,B)**: [ _______ ]
- **LCM(A,B)**: [ _______ ]
[Submit Question]
### Explanation of Terms:
- **Greatest Common Factor (GCF)**: The largest positive integer that divides each of the given numbers without a remainder.
- **Least Common Multiple (LCM)**: The smallest positive integer that is divisible by each of the given numbers.
Analyzing the prime factorization provided:
- The prime factors for \(A\) are \(3^3\), \(5^3\), \(7^2\), \(11^3\), and \(13\).
- The prime factors for \(B\) are \(2\), \(3^3\), and \(13^3\).
To find the GCF and LCM:
- **GCF**: Take the lowest power of each prime common to both numbers.
- **LCM**: Take the highest power of each prime that appears in either number.
Please input the correct GCF and LCM values in their respective fields and click "Submit Question" to check your answers.
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