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he 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) ar СМа, b, c). a) If a = 32 . 5² .73 b = 33.51.71, and c = 22 • 5³ • 7', compute GCD(a, b, c) and LCM(a, b, c). b)ls 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. a) GCD(a, b, c) = U

he 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) ar СМа, b, c). a) If a = 32 . 5² .73 b = 33.51.71, and c = 22 • 5³ • 7', compute GCD(a, b, c) and LCM(a, b, c). b)ls 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. a) GCD(a, b, c) = U

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 66E
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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 = 32 . 52 .7°, b = 33 •51 • 7', and c= 22 .53.71, compute GCD(a, b, c) and LCM(a, b, c). (b)ls 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. (a) GCD(a, b, c) = O LCM(a, b, c) = (b) Choose the correct answer below. O A. Yes. Since the GCD is found using the larger exponents and the LCM is found using the smaller exponents, it must be true that GCD(a, b, c) • LCM(a, b, c) = abc. O B. Yes. It is shown in part (a) that GCD(a, b, c) • LCM(a, b, c) = abc. O C. Yes. Since the GCD is found using the smaller exponents and the LCM is found using the larger exponents, it must be true that GCD(a, b, c) • LCM(a, b, c) = abc. O D. No, it is not necessarily true that GCD(a, b. c) • LCM(a, b. c) = abc.
Transcribed Image Text: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 = 32 . 52 .7°, b = 33 •51 • 7', and c= 22 .53.71, compute GCD(a, b, c) and LCM(a, b, c). (b)ls 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. (a) GCD(a, b, c) = O LCM(a, b, c) = (b) Choose the correct answer below. O A. Yes. Since the GCD is found using the larger exponents and the LCM is found using the smaller exponents, it must be true that GCD(a, b, c) • LCM(a, b, c) = abc. O B. Yes. It is shown in part (a) that GCD(a, b, c) • LCM(a, b, c) = abc. O C. Yes. Since the GCD is found using the smaller exponents and the LCM is found using the larger exponents, it must be true that GCD(a, b, c) • LCM(a, b, c) = abc. O D. No, it is not necessarily true that GCD(a, b. c) • LCM(a, b. c) = abc.
(c) Choose the correct answer below O A. r=3, s= 5, t=7 O B. r= 3, s =9, t= 5 O C. r=8, s=2, t= 8 O D. r=7, s= 3, t = 7
Transcribed Image Text:(c) Choose the correct answer below O A. r=3, s= 5, t=7 O B. r= 3, s =9, t= 5 O C. r=8, s=2, t= 8 O D. r=7, s= 3, t = 7
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