1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Harrizon [31]
2 years ago
11

Starting with 54 and 36, replace the 54 with the greatest common divisor of 54 and 36, obtaining a1, and then replace 36 with th

e least common multiple of 54 and 36, obtaining b1. Repeat the procedure on a1 and b1, obtaining a2 and b2 and so on. Starting with a1 and b1, what is the least number of times this procedure can be repeated until a1 and b1 are obtained again?
Mathematics
1 answer:
nalin [4]2 years ago
6 0

Answer:

1 time

Step-by-step explanation:

Given numbers are 54 and 36.

The greatest common divisor of 54 and 36 = 18

So, a_1 = 18.

The least common multiple of 54 and 36 = 108

So, b_1 = 108.

As 54 is replaced by a_1 and 36 is replaced by b_1, so after applying the given procedure, the new number is

(a_1, b_1)=(18, 108)\cdots(i)

Now, apply the same procedure, to get a_2 and b_2.

The greatest common divisor of 18 and 108 = 18

So, a_2 = 18.

The least common multiple of 18 and 108 = 108

So, b_2 = 108.

As a_1 is replaced by a_2 and b_1 is replaced by b_2, so after applying the given procedure, the new number is

(a_2, b_2)=(18, 108) which is the same as in equation (i)

Hence, after applying the procedure 1 time after (a_1, b_1), the obtained number (a_2, b_2) is the same as (a_1,b_1).

You might be interested in
PLEASE HELP!!!! 20 POINTS!!!
Vlad1618 [11]
Mass = density* volume
since density= mass/volume then mass/volume*volume=mass
= 4.5*0.4 =  1.80g

6 0
3 years ago
Evaluate.<br>  <br> 4⋅(<br> 1<br> 4<br> −3<br><br> )+12
Artemon [7]
4.(14-3) + 12
4.11 + 12
44 + 12
56
3 0
3 years ago
Read 2 more answers
The decimal 0.4444 is an example of what kind of number
Slav-nsk [51]
That would be a decimal!
5 0
2 years ago
Which of the following describes an angle with a vertex at Z?
Tresset [83]
B is the answer and why is bc I took the quiz
5 0
2 years ago
Given the vector (4|3) and the transformation matrix (0|1|-1|0), which vector is the imagine after applying the transformation t
horrorfan [7]

Answer:

C.(3|-4)

Step-by-step explanation:

Given the vector:

\left[\begin{array}{ccc}4\\3\end{array}\right]

The transformation Matrix is:

\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]

The image of the vector after applying the transformation will be:

\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\left[\begin{array}{ccc}4\\3\end{array}\right]\\\\=\left[\begin{array}{ccc}0*4+1*3\\-1*4+0*3\end{array}\right]\\\\=\left[\begin{array}{ccc}3\\-4\end{array}\right]

The correct option is C

7 0
3 years ago
Other questions:
  • Mason plays a game by flipping two fair coins. He wins the game if both coins land facing heads up. If Mason plays 200 times, ho
    8·2 answers
  • 2. A company that produces fine crystal knows from experience that 10% of its goblets have cosmetic flaws and must be classified
    13·2 answers
  • I need help with “B”
    9·1 answer
  • Find the slope between 2 points. <br> (16, 12) (40,18)
    15·1 answer
  • An expression is shown below:
    9·2 answers
  • Help plssssssssssssssssssss
    6·2 answers
  • A die was rolled eight times. The rolls were 2, 2, 3, 4, 4, 5, 6, and 6. What is the mean absolute deviation for this data? A) 1
    9·1 answer
  • The Lopez family is driving to the state fair. First, they drove 32 kilometers to stop for a snack. Then, they drove another 35
    5·2 answers
  • What is the interquartile range (IQR) of the data set represent by this box plot
    14·1 answer
  • Let's calculate the surface of the ABC triangle from the image if the area of the triangle DBC is 40 square unit,| BC| = 8i| AB|
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!