Least common multiple (LCM) - practice problems - page 4 of 13
The Least Common Multiple (LCM) of integers is the smallest number that is divisible by these numbers without a remainder. Example: LCM(12, 15) = 60.Number of problems found: 252
- MO C–I–1 2018
An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones. - Relay teams
There are 159 students to be grouped into relay teams. Each team should have the same number of students. Can each team have 3,5 or 6 students? Explain. - Exercisers
How many exercisers are in the gym (minimum number) if there is one left after ordering into three, four, and five steps? - Athletes
Athletes at the stadium could enter two-steps, three-steps, four-steps, five-steps, and six-steps. There were more than 100 but less than 200. How many athletes were there? - Balls groups
Karel pulled the balls out of his pocket and divided them into groups. He could divide them in four, six, or seven, and no ball ever left. How little could be a ball? - Game room
The winner can take the win in three types of jettons with value 3, 30, and 100 dollars. What is the minimum value of win payable in these values of jettons? - The King
The King wants to divide his sons equally. He has 42 rubies and 45 diamonds. How many sons and how will they share them? - Three-digit 8002
Find the largest three-digit number that gives the remainder 1 when divided by three, gives the remainder 2 when divided by four, gives the remainder 3 when divided by five, and gives the remainder 4 when divided by six. - What is 20
What is the least number that should be added to 2497 so that the sum of the digits is divisible by 5, 6, and 10? - Runners circle
Pepa circles the track in 36 seconds. Kamil in 42 seconds. They started together. How many seconds will we meet again at the start? - Nuts
How many must we have at least nuts if we can equally divide it to 10 children, 12 children, or 15 children and any nuts left? - Smallest 4432
What is the smallest number of members of a dance group with the same number of guys and girls, and at the same time they can form groups of three or five dancers while dancing? - Ronald 2
Ronald and Tim both did their laundry today. Ronald does laundry every 6 days, and Tim does laundry every 9 days. How many days will it be until Ronald and Tim both do laundry on the same day? - Lamps on playground
The playground has the shape of a rectangle of 36 x 50m. After how many meters can place the lamps on its 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? - Tram stop
The blue tram stops every 12 minutes, the red one for 8 minutes. At 8 o'clock, they left the stop together. How many times do they meet at a stop before 11 AM? - Class 9A
On the final certificate, one-quarter of the class 9A marked “C” in mathematics, the seventh mark “C” from the Czech language, and two students failed in chemistry. How many students attend class 9A? - Buses 4
Intervals: 1st bus 40 min. 2nd bus 2h 3rd bud 20min How long will it take them to meet - as soon as possible? - Buses
At the bus stop at 10 o'clock met buses No. 2 and No. 9. Bus number 2 runs at an interval of 4 minutes and bus number 9 at intervals of 9 minutes. How many times does the bus meet at 18:00 local time? - Buses
Buses Ikarus and Karosa simultaneously started at 8:00 from the final station. Ikarus is returned to the station after 30 minutes. Karosa after 45 minutes. At what time do both buses again return to the station? - Square room
What is the size of the smallest square room, which can be paved with tiles with dimensions of 55 cm and 45 cm? How many such tiles are needed?
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