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What are the greatest common divisors and the least common mutiples of each of the following pairs of integers? You can enter the exponent by typing "^" symbol, for example, type 2^3 for 2³. (a) 33-54.73-133 and 21.33.51.11². 13². gcd = lcm = (b) 22.5¹.72.114. 13³ and 22-33-54-11³ - 132. gcd = lcm =

What are the greatest common divisors and the least common mutiples of each of the following pairs of integers? You can enter the exponent by typing "^" symbol, for example, type 2^3 for 2³. (a) 33-54.73-133 and 21.33.51.11². 13². gcd = lcm = (b) 22.5¹.72.114. 13³ and 22-33-54-11³ - 132. gcd = lcm =

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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What are the greatest common divisors and the least common mutiples of each of the following pairs of integers? You can enter the exponent by typing "^" symbol, for example, type 2^3 for 2³. (a) 33-54.73-133 and 21.33.51.11². 13². gcd = lcm = (b) 22.5¹.72.114-13³ and 22-33-54-11³ - 13². gcd = Icm =
Transcribed Image Text:What are the greatest common divisors and the least common mutiples of each of the following pairs of integers? You can enter the exponent by typing "^" symbol, for example, type 2^3 for 2³. (a) 33-54.73-133 and 21.33.51.11². 13². gcd = lcm = (b) 22.5¹.72.114-13³ and 22-33-54-11³ - 13². gcd = Icm =
Expert Solution
Step 1

a)gcd=3^3*5^1*13^2

Gcd=27*5*169

Gcd=22815

 

To find the GCD, we take the lowest power of each prime factor that appears in both factorizations:

 

GCD = 3^3 × 5 × 13^2 =22815

 

Therefore, the GCD is 2535.

2×3×3×3×5×11×11×13×13 = 2 × 3^3 × 5 × 11^2 × 13^2

 

Now, we can find the LCM by taking the highest power of each prime factor that appears in either of the two factorizations:

 2 × 3^3 × 5 × 7^3 × 11^2 × 13^3 × 13^2 = 2 × 3^3 × 5 × 7^3 × 11^2 × 13^3 × 13^2

 

Therefore, the LCM is 2 × 3^3 × 5 × 7^3 × 11^2 × 13^3 × 13^2.

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