The notions of the greatest common divisor and the least common multiple extend naturally to more than two numbers. Moreover, the prime-factorization method extends naturally to finding GCD(a, b, c) and LCM(a, b, c). (a) If a = 21 •52 . 7ª, b= 23 • 53 • 7², and c= 21 • 32 • 53, compute GCD(a, b, c) and LCM(a, b, c). (b) Is it necessarily true that GCD(a, b, c) • LCM(a, b, c) = abc? (c) Find numbers r. S. and t such that GCD(r. s. t) • LCM(r. s. t) = rst

The notions of the greatest common divisor and the least common multiple extend naturally to more than two numbers. Moreover, the prime-factorization method extends naturally to finding GCD(a, b, c) and LCM(a, b, c). (a) If a = 21 •52 . 7ª, b= 23 • 53 • 7², and c= 21 • 32 • 53, compute GCD(a, b, c) and LCM(a, b, c). (b) Is it necessarily true that GCD(a, b, c) • LCM(a, b, c) = abc? (c) Find numbers r. S. and t such that GCD(r. s. t) • LCM(r. s. t) = rst

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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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

The notions of the greatest common divisor and the least common multiple extend naturally to more than two numbers. Moreover, the prime-factorization
method extends naturally to finding GCD(a, b, c) and LCM(a, b, c).
(a) If a = 21 .52 .71, b= 23 . 53. 7², and c = 21 • 3² .53, compute GCD(a, b, c) and LCM(a, b, c).
(b) Is it necessarily true that GCD(a, b, c) • LCM(a, b, c) = abc?
(c) Find numbers r. s. and t such that GCD(r. s. t) • LCM(r. s. t) = rst.

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