Clock's gears

In the clock machine, three gears fit together. The largest has 168 teeth, the middle 90 teeth, and the smallest 48 teeth. The middle wheel turns around its axis in 90 seconds. How many times during the day do all the gears meet in the starting position?

Correct result:

n =  17

Solution:

168=2337 90=2325 48=243 LCM(168,90,48)=243257=5040  z=LCM(168,90,48)=5040  v=90/90=1 z/s  n1=24 3600z/v=24 36005040/1120717.1429  n=n1=17.1429=17168=2^3 \cdot 3 \cdot 7 \ \\ 90=2 \cdot 3^2 \cdot 5 \ \\ 48=2^4 \cdot 3 \ \\ LCM(168, 90, 48)=2^4 \cdot 3^2 \cdot 5 \cdot 7=5040 \ \\ \ \\ z=LCM(168,90,48)=5040 \ \\ \ \\ v=90/90=1 \ \text{z/s} \ \\ \ \\ n_{1}=\dfrac{ 24 \cdot \ 3600 }{ z / v }=\dfrac{ 24 \cdot \ 3600 }{ 5040 / 1 } \doteq \dfrac{ 120 }{ 7 } \doteq 17.1429 \ \\ \ \\ n=\lfloor n_{1} \rfloor=\lfloor 17.1429 \rfloor=17



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Do you want to calculate least common multiple two or more numbers?
Do you want to convert velocity (speed) units?
Do you want to perform natural numbers division - find the quotient and remainder?
Do you want to convert time units like minutes to seconds?

Next similar math problems:

  • Biketrial
    cyklo Kamil was biketrial. Before hill he set the forward gear with 42 teeth and the back with 35 teeth. After how many exercises (rotation) of the front wheel both wheels reach the same position?
  • Three Titanics
    Titanic Three steamers sailed from the same port on the same day. The first came back on the third day, fourth 4th day and the third returned sixth day. How many days after leaving the steamers met again in the harbor?
  • Game room
    roulette Winner can took win in three types of jettons with value 3, 30 and 100 dollars. What is minimal value of win payable in this values of jettons?
  • Lamps on playground
    lamp The playground has the shape of a rectangle 36 x 50m. After how many meters will he place the lamps on his lighting, if the distances between them are to be the same on both sides if the builders want to use the smallest possible number of lamps?
  • LCM of two number
    numbers2_19 Find the smallest multiple of 63 and 147
  • Lcm 2
    lcm Create the smallest possible number that is divisible by numbers 5,8,9,4,3
  • Dance ensemble
    dancers_1 The dance ensemble took the stage in pairs. During dancing, the dancers gradually formed groups of four, six and nine. How many dancers have an ensemble?
  • Six-digit primes
    numberline_1 Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they?
  • Cyclist vs car
    car2 Cyclist rode out of the city at 18 km/h. 1 hour 30 minutes behind him started car and caught up with the cyclist in 50 minutes. How fast was driving the car? Where (what kilometer) from the city car overtook a cyclist?
  • Apples 2
    jableka How many minimum apples are in the cart, if possible is completely divided into packages of 6, 14 and 21 apples?
  • Trams
    elektricka Trams have an average speed 23 km/h and run in tact 14 minutes. Pedestrian walking speed is 3.3 km/h. At what intervals trams outrun pedestrian?
  • Primes 2
    prime_table Which prime numbers is number 2025 divisible?
  • Dance group
    dancers The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
  • The florist
    ruze_6 The florist had 200 roses in the morning. During the day, more than half sold it. From the remaining roses, it will tie the bouquet. If a bouquet of 3, 4, 5 or 6 roses are bound, one always remains. How many roses from the morning shipment sold?
  • MO C–I–1 2018
    numbers_49 An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
  • 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
  • Plums
    svestka In the bowl are plums. How many would be there if we can divide it equally among 8, 10 and 11 children?