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) andLCM(a, 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) = |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.OC. 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.D.No it is not necessarily true that GCD(a b c)•I CM(a b c) = abcOO C (c) Choose the correct answer below.O A. r=3, s=5, t=7O B. r= 3, s =9, t= 5O C. r=8, s=2, t= 8O D. r=7, s= 3, t= 7

Note: As per Bartleby’s guideline for more than one questions only first is to be answered please…

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) ar LCM(a, b, c). (a) If a = 32 . 52 . 73 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.

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) ar LCM(a, b, c). (a) If a = 32 . 52 . 73 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.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: The following decision algorithm, A, is proposed for the perfect square problem: Compute x^2 for…

A: In studying computational complexity, we study the complexity of algorithm by comparing with known…

Q: Use the extended Euclidean algorithm to find the greatest common divisor of 8,820 and 1,005 and…

A: To use the Extended Euclidean Algorithm to find the gcd8820, 1005 and express the linear combination…

Q: each expression. – 76² + 76) + (5b² – 36* – 36) 4) (6v + 3v² – 6v) – (7»

Q: 7) Note that -2 is a square modulo 11. Indeed, 82 +2 = 6.11. Use this information, and the method of…

A: To use method of descent to construct a solution of x2+2y2=11 Now, it is known that -2 is a square…

Q: In an educational institution, the stipends earned by the students in the first year summer…

A: Given: The stipends earned by the students as follows,Stipend earned (in Z) Number of students0 —…

Q: Determine the greatest common divisor GCD (xn-1,Xm-1) where m, n are nonzero natural numbers.…

A: We have to determine the greatest common divisor of xn-1, xm-1, where m, n are nonzero natural…

Q: If there are (2n+1) term in AP.then prove that the ratio of the sum of odd terms and the sum of even…

Q: What is p(3, 2)? [Hint: Each sample of size 6 is equallylikely to be selected. Therefore, p(3, 2) 5…

Q: In Fermat's Factorization method, why does n = ab can be transformed to ?

A: Fermat’s Factorization method is based on the representation of an odd integer as the difference of…

Q: 2. Compute the ged of the number below using 1) factorization, 2) using Euclid's division algo-…

Q: Graph the Imag ol the trapemid below uing a scale factor of 1/4

Q: You have a large 2 x n checkerboard, and you want to cover its 2n squares using the available…

A: Given that : an= 2×n In-order to find the values of a1,a2 and a3; a1=2*1=2 a2=2*2=4 a3=2*3=6…

Q: (a) Write 23 as a sum of distinct powers of 2. (b) Use the fast factoring algorithm to compute 323…

A: To represent 23 as a sum of distinct powers of 2, we can use the binary representation of the…

Q: This question is about the division algorithm in Z[√2]. Let w = (-3+8√2) and 2 = (6-7√2). (0) Find…

A: there are some problems in question. Please find the details in next steps

Q: Compute Pearson's r demonminator with the computational formula and use 4 decimal places for all…

A: We have given that data stress : exam scores: 5 4 6 5 6 2 4…

Q: 2. (i) (1 2 3 4 5) (2 5 4 3 1) and (1 5 3 2 4) Find the product of the permutations: (a, az ... Ax)…

A: NOTE- Since the terms in the last bracket of first part are not clear, so solving just second part…

Q: 4 Suppose we have 3000 identical sheets separated into packs of 25 sheets each. Use generating…

A: In the question, it has to be at least 150 sheets and no more than 1000 sheets. Otherwise question…

Q: Create a box-grid with 10 rows and 9 columns (eg. using google Sheets) and, starting from the upper…

A: We will use basic knowledge of number theory to answer this question in google sheets.

Q: For a = 2695, b = 1820, use the prime factorizations to find lcm(a, b) and gcd(a, b). Verify that ab…

A: Given thata = 2695 and b = 1820We have to find lcm(a, b) and gcd(a, b) by using prime…

Q: 8. Since the factors of (7-2)! can be rearranged in the following manner (7-2)!= it is easily…

Q: "hich diagram shows one way to model factors of 165? 10 10 7. CLEA 10 + 5 10 + 1 10 10-10 10-5 10…

A: See the details solution in below

Q: (13),0 - (159), using excess-3 codes with 9's complement method.

Q: When x is divided by 7, the remainder is 5. What is the remainder when 5x is divided by 7? Moreover,…

Q: (a) If a, b,c € Z+ and a +b=c then (c,[a, b)) = (a, b).

A: As you asked multiple questions , so I solved only the first one.

Q: Use the factorization A = PDP - 1 to compute A", where k represents an arbitrary integer. а 11(b -а)…

A: 1st we will derive a formula for Ak and then find its value using that

Q: bute 80 identical pencils in a class consisting of 10 boys and 20 girls in such a way that each of…

A: Given:- Number of boys=10 Number of girls = 20 Number of Pencils=80

Q: 5. Find LU Factorizatioon of A = [5 2 1 1 3 2 7 1 2 3 2 1- Show the work!

Q: this website has given me the wrong answer two times, in the second question stated, i have asked…

A: IntroductionTo explain why successive composites that give the sequence of GPFs 41, 19, 79 must all…

Concept explainers

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 = 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) = |
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.
OC. 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.
D.
No it is not necessarily true that GCD(a b c)•I CM(a b c) = abc
OO C

(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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Introduction:

VIEW

Calculation:

VIEW

Conclusion:

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Fundamental Counting Principle$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

9/ Three young brother-sister pairs from different families need to take a trip in a van. These sixchildren will occupy the second and third rows in the van, each of which has three seats. Toavoid disruptions, the siblings may not sit right next to each other in a row and no child may sitdirectly in front of his or her sibling. How many seating arrangements are possible for this trip? 10/ 11. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?
don't copy
We want to find the number of ways in which 3r balls can be selected from 2r red ballsand 2r blue balls. Find the generating function corresponding to the above problem in closed form.
If x is the greatest prime factor of 39 and y is the greatest prime factor of 72, what is the value of x + y? AO 16 BO 111 49 25 On a certain test, each of five students scored between 0 and 50, inclusive (meaning two students can have the same score). If their average score is 40, what is the greatest possible number of students who could have scored a 25? AO Four BO One CO Three DO Two U
3) If the bisection method is used to solve the equation 3x²= e* in [3.5,4] then the value of c₂ is O 3.7188 O 2.8871 O 2.7188 O not in the options above
(2) 3.2 Use prime factors to determine the HCF of 90 and 126 (4)
Suppose there are two boxes; in box 1 there are 3 times more green balls than red balls, and in box 2 there are 5 red balls and 8 green ones. We choose one of the boxes at random (that is P(B1) = P(B2) = 0.5), and then 3 balls are randomly taken from that box with replacement. Notice that the actual number of colored balls in box 1 is not given, which causes no problem since the drawings are done with replacement. 1. Calculate the following probabilities by theoretical approach and include the calculations and the results in your report: a) The probability that 2 red balls and 1 green ball are drawn (P(2R n 1G) =?) b) If all 3 balls are green what is the probability that box 1 was chosen (P(B1|3G) =?)
(3. Find the greatest common divisor and least common multiple of a = 2338712132 and b = 365511213.
Use the extended Euclidean algorithm to find the greatest common divisor of 9,090 and 936 and express it as a linear combination of 9,090 and 936. Step 1: Find ₁ and ₁ so that 9,090 = 936 9₁+₁, where 0 ≤r₁ < 936. Then 1 = 9,090 - 936 9₁ = Step 2: Find 92 and r₂ so that 936 = ₁.9₂ +r₂, where 0≤r₂ <1 Then = 936- 2 •92 Step 3: Find 93 and r3 so that r₁ = r₂ 93 +r3, where 0≤r3
The global error in a Runge-Kutta 4th order method is "big O" of 4 O 4h h 4
1) Come up with a 2 x 2 contingency table for which p^1=p^2, and for which the row and column totals are notthe same. Now calculate χ2*. Are you surprised? Why or why not?
(a) Use the prime factorizations of 84 and 264 to find gcd(84,264) and lcm(84,264). (b) Describe a general method for finding gcd(a,b) and lcm(a,b) if you know the prime factorizations of a and b.