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Using prime factorization, find gcd(120, 500) and lcm(120, 500).

Using prime factorization, find gcd(120, 500) and lcm(120, 500).

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Problem 4.** Using prime factorization, find gcd(120, 500) and lcm(120, 500). Explanation: To solve this problem, follow these steps: 1. **Prime Factorization**: - Find the prime factors of 120 and 500. - 120: \(2^3 \times 3 \times 5\) - 500: \(2^2 \times 5^3\) 2. **Greatest Common Divisor (gcd)**: - Identify the lowest power of all common prime factors. - Common factors: \(2^2\) and \(5\) - gcd(120, 500) = \(2^2 \times 5 = 20\) 3. **Least Common Multiple (lcm)**: - Identify the highest power of all prime factors present in both numbers. - Highest powers: \(2^3, 3^1, 5^3\) - lcm(120, 500) = \(2^3 \times 3 \times 5^3 = 3000\) This problem demonstrates the process of finding both the greatest common divisor and the least common multiple using prime factorization.
Transcribed Image Text:**Problem 4.** Using prime factorization, find gcd(120, 500) and lcm(120, 500). Explanation: To solve this problem, follow these steps: 1. **Prime Factorization**: - Find the prime factors of 120 and 500. - 120: \(2^3 \times 3 \times 5\) - 500: \(2^2 \times 5^3\) 2. **Greatest Common Divisor (gcd)**: - Identify the lowest power of all common prime factors. - Common factors: \(2^2\) and \(5\) - gcd(120, 500) = \(2^2 \times 5 = 20\) 3. **Least Common Multiple (lcm)**: - Identify the highest power of all prime factors present in both numbers. - Highest powers: \(2^3, 3^1, 5^3\) - lcm(120, 500) = \(2^3 \times 3 \times 5^3 = 3000\) This problem demonstrates the process of finding both the greatest common divisor and the least common multiple using prime factorization.
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