Explanation Given: The given numbers are 18 and 12. Approach: The Intersection of Sets Method: In this method first write all the non-zero whole numbers as a multiple of both the first number as well as the second numbers, then find the multiples of numbers which are common to both the sets. Now pick the least number in order to get the LCM whereas, write all the divisor of both the numbers and take the highest number common in the divisor as a GCD of the given numbers. The sets of non-zero whole number multiple and divisor of n can be denoted by M n , and D n . Calculation: Consider the given numbers 18 and 12. Now, in order to get the GCD of the numbers 18 and 12 write all the divisor of 18 and 12 by using Intersection of Sets Method which can be denoted by D 18 and D 12 respectively. D 18 = { 1 , 2 , 3 , 6 , 9 , 18 } and D 12 = { 1 , 2 , 3 , 4 , 6 , 12 } Take the sets of all common non-zero whole number divisors of 18 and 12 as, D To determine (b) To find: The GCD and the LCM of the numbers 20 and 36 with the help of intersection-of-sets method. To determine (c) To find: The GCD and the LCM of the numbers 8, 24 and 64 with the help of intersection-of-sets method. To determine (d) To find: The GCD and the LCM of the numbers 7 and 9 with the help of intersection-of-sets method.

A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)

13th Edition

ISBN: 9780135183885

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott, Barbara Boschmans

Publisher: PEARSON

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 4.3A, Problem 2A

To determine

(a)

To find:

The GCD and the LCM of the numbers 18 and 12 with the help of intersection-of-sets method.

To determine

(b)

To find:

The GCD and the LCM of the numbers 20 and 36 with the help of intersection-of-sets method.

To determine

(c)

To find:

The GCD and the LCM of the numbers 8, 24 and 64 with the help of intersection-of-sets method.

To determine

(d)

To find:

The GCD and the LCM of the numbers 7 and 9 with the help of intersection-of-sets method.

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Chapter 4.3A, Problem 1A

Chapter 4.3A, Problem 3A

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(a) To find: The GCD and the LCM of the numbers 18 and 12 with the help of intersection-of-sets method.

Solution Summary: The author explains how to find the GCD and LCM of the numbers 18 and 12 with the help of intersection-of-sets method.

Concept explainers

(a) To find: The GCD and the LCM of the numbers 18 and 12 with the help of intersection-of-sets method.

(b) To find: The GCD and the LCM of the numbers 20 and 36 with the help of intersection-of-sets method.

(c) To find: The GCD and the LCM of the numbers 8, 24 and 64 with the help of intersection-of-sets method.

(d) To find: The GCD and the LCM of the numbers 7 and 9 with the help of intersection-of-sets method.

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Chapter 4 Solutions

(a)

To find:

The GCD and the LCM of the numbers 18 and 12 with the help of intersection-of-sets method.

(b)

To find:

The GCD and the LCM of the numbers 20 and 36 with the help of intersection-of-sets method.

(c)

To find:

The GCD and the LCM of the numbers 8, 24 and 64 with the help of intersection-of-sets method.

(d)

To find:

The GCD and the LCM of the numbers 7 and 9 with the help of intersection-of-sets method.