answer.
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
coldgirl [10]
1 year ago
14

The greatest common divisor of two positive integers less than $100$ is equal to $3$. Their least common multiple is twelve time

s one of the integers. What is the largest possible sum of the two integers?
Mathematics
1 answer:
tangare [24]1 year ago
3 0

Answer:

129

Step-by-step explanation:

Let a and b be two numbers.

We have been given that the greatest common divisor of two positive integers less than 100 is equal to 3. We can represent this information as GCD(a,b)=3.

Their least common multiple is twelve times one of the integers. We can represent this information as LCM(a,b)=12a.

Now, we will use property GCD(x,y)*LCM(x,y)=xy.

Upon substituting our given values, we will get:

3*12a=ab

36a=ab

Switch sides:

ab=36a

\frac{ab}{a}=\frac{36a}{a}

b=36

Now, we need to find a number less than 100, which is co-prime with 12 after dividing by 3.

The greatest multiple of 3 less than 100 is 99, but it is not co-prime with 12 after dividing by 3.

Similarly 96 is also not co-prime with 12 after dividing by 3.

We know that greatest multiple of 3 (less than 100), which is co-prime with 12, is 93.

Let us add 36 and 93 to find the largest possible sum of the required two integers as:

36+93=129

Therefore, the required largest possible sum of the two integers is 129.

You might be interested in
A second grade student is 4 feet tall. Her teacher is 5 2/3 feet tall. How many times as tall as the student is the teacher
Alchen [17]

Answer:

The teacher is 1.416667 times taller than the student

Step-by-step explanation:

(5 2/3)/4

=1.416667

4 0
1 year ago
Match the information with the locations where the information belongs in a resume.
Marina86 [1]
Your question is in the wrong category but I will try to help. 1. objective 2. awards 4. skill summary I've been really thinking about 3 and 5 because of their close. I think it might be 3. education maybe?

8 0
1 year ago
Read 2 more answers
A bar graph titled Album Type Sold per Year has year on the x-axis and number of albums sold on the y-axis. For C D s, in 2008 t
stira [4]

Answer:

True, True, False, True, False, True

Step-by-step explanation:

<u>CDs have a higher mean than digital</u>

<u />

Let's check.  CD mean is (1000 + 800 + 800 + 600 + 400 + 200)/6 = 633.33

Digital mean: (100 + 300 + 300 + 500 + 700 + 900)/6 = 466.67

CD's mean is higher.  Since you are dividing byt he same number you also could have just added the amount and found which was a larger number.  But yes, this is true.

<u>The range of digital is 800</u>

<u />

The range is the highest number inus the lowest number.  For digital the highest is 900 and lowest is 100 so the ange is 900-100 = 800.  So this is true.

<u>The median of CDs is 400. </u>

<u />

The median is the middle value for odd numbers of values, or the average of the two middle values.  6 total values means you have to take the third and fourth and average them.  in CDs the middle values are 800 and 600, the average is 700, so that is what the median is.  this is false.

<u>Both have the same interquartile range. </u>

<u />

Interquartile range is to find the middle number or numbers like in median, then take the two parts it is split into and find the "median" of those.  Then subtract the larger one fromt he smaller one.

IQR of CD the first half is 200, 400, 600 so the middle here is 400, second half has a middle number of 800 so IQR here is 800-400=400

IQR of digital is 700-300 = 400 so yes both are the same.

<u>Both have the same median</u>

<u />

We know the medan of CDs is 700 then findign the median of digital is (300+500)/2 = 400.  So no, the medians are not the same.

<u>Digital’s mean is around 467. </u>

<u />

We founf the mean for digital to be 466.67 which rounds up to 467, So I would say it is true.

8 0
2 years ago
Read 2 more answers
a shark can swim 24 meters in 36 seconds. at this rate, how far, in meters, will the shark swim in 2 minutes?​
blagie [28]

Answer:80 meters

Step-by-step explanation: 24 meters = 36 secs

2 mins = 120 secs

Cross multiply

24×120/36

= 80 meters

Hope I helped you!!

8 0
2 years ago
Read 2 more answers
In triangle PQR, PS, QT,and RU are the medians , and PS and QT intersect at the point (4,5)
jekas [21]
We are given with a triangle and three medians. The intersection of the two medians is also given which is (4,5). What is asked is the intersection between another pair of medians. Since the medians of a triangle intersect at the centroid of a triangle, the intersection is also
<span>B. (4, 5)</span>
7 0
1 year ago
Read 2 more answers
Other questions:
  • What did the athlete order when he needed a huge helping of mashed potatoes? unscramble the following letters: p, p, r, o, m, n,
    13·1 answer
  • The stadium owner is considering an offer from Reliable Tools to change the name to Reliable Stadium. The company is offering to
    5·2 answers
  • Divide $3,300 into three parts whose ratio is 1:3:7.
    10·1 answer
  • Trevor Ariza is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next on
    11·2 answers
  • Cheese sticks that were previously priced at "5 for $1" are now "4 for $1". Find each percent of change . Find the percent decre
    13·1 answer
  • Ritu started a business and borrowed a certain sum at 14% per annum for 1 year, the interest being compounded semi annually. If
    15·1 answer
  • Suppose F⃗ (x,y)=⟨ex,ey⟩F→(x,y)=⟨ex,ey⟩ and CC is the portion of the ellipse centered at the origin from the point (0,1)(0,1) to
    5·1 answer
  • Triangle OMG has vertices at O(−3,3), M(4,2), and G(−3,1). Point G is rotated 90° counterclockwise around the origin, forming G'
    5·1 answer
  • Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. How many total kilograms of candy did he buy?
    12·1 answer
  • You score 90 on the midterm, 60 on the final, and 80 on the class project. What is your average score if the midterm is worth 30
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!