Reminder and quotient

There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1.

Correct result:

R =  946

Solution:

A=135 B=315  135=335 315=3257 LCM(135,315)=3357=945  x=LCM(A,B)=LCM(135,315)=945  R=x+1=945+1=946A=135 \ \\ B=315 \ \\ \ \\ 135=3^3 \cdot 5 \ \\ 315=3^2 \cdot 5 \cdot 7 \ \\ LCM(135, 315)=3^3 \cdot 5 \cdot 7=945 \ \\ \ \\ x=LCM(A,B)=LCM(135,315)=945 \ \\ \ \\ R=x+1=945+1=946



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 2 comments:
#
Math student
Calculatin is all wrong.
Smallest number after 1 is 2 .
And 2 also give me the remainder 1.
135/2 and 315/2 calculate yourself.

#
Dr Math
please read carefully  R:A, R:B , R=2:

2:135 is 0 and reminder 2 !!!

avatar









Tips to related online calculators
Do you want to calculate least common multiple two or more numbers?
Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.
Do you want to perform natural numbers division - find the quotient and remainder?

Next similar math problems:

  • Divisibility
    divisibility Is the number 761082 exactly divisible by 9? (the result is the integer and/or remainder is zero)
  • Odd/even number
    numbers2_49 Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat the process with your new number. If you keep going, you'll eventually end up at 1. Every time. Prove. ..
  • Diophantus
    diofantos_1 We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A. D. Thanks to an admirer of his, who described his life through an algebraic riddle, we know at least something about his life. Diophantus's youth las
  • Reminder and quotient
    prime_5 There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S, D:S are with the remainder of 1,
  • School year
    zosity At the beginning of the school year, 396 notebooks and 252 textbooks are ready to be distributed in the classroom. All pupils receive the same number of notebooks and the same amount of textbooks. How many pupils are there in the class if you know that th
  • Meadow
    ovce-miestami-baran On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together?
  • Lcm 2
    lcm Create the smallest possible number that is divisible by numbers 5,8,9,4,3
  • The tickets
    oriesky The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
  • Numbers
    ten Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
  • Z9–I–4 MO 2017
    vlak2 Numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of each of the three was equal to the sum of the remaining two. The conduct
  • Engineer Kažimír
    demagog_smer_1 The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri
  • Pool
    pool If water flows into the pool by two inlets, fill the whole for 19 hours. The first inlet filled pool 5 hour longer than the second. How long pool take to fill with two inlets separately?
  • Intelligence test
    test Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus 7 questions, Jano to a third plus 18 questions, Karol to a quarter plus 21 questions and Risho to a fifth plus 25 questions. After the test, Ka
  • Z9-I-4
    numbers_30 Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Final
  • Endless lego set
    lego_2 The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. The
  • Unknown number
    iks-icon Samuel wrote unknown number. Then he had add 200000 to the number and the result multiply by three. When it calculated he was surprised, because the result would have received anyway, if write digit to the end of original number. Find unknown number.
  • Number train
    train2 The numbers 1,2,3,4,5,6,7,8 and 9 traveled by train. The train had three cars and each was carrying just three numbers. No. 1 rode in the first carriage, and in the last carriage was all odd numbers. The conductor calculated sum of the numbers in the firs