Divisibility + least common multiple (LCM) - practice problems - page 2 of 5
Number of problems found: 94
- Destination 18323
The family went on a trip to a ruin 6 km away. The father had a step length of 0.75 m, the mother of 0.6 m, and little Eva 50 cm. They went out on the same step. How many times did their steps retrace before reaching their destination? - Intelligence test
Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus seven 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 tes - Length of a string
What are the smallest string length we can cut into 18 equal parts and even 27 equal parts (in decimeters)? - Matemakak 9432
The cookbook by Matěj Matemakak says: The greatest common divisor of flour weight and sugar weight is 15, the greatest common divisor of sugar weight and lemon peel weight is 6, the product of sugar weight and lemon peel weight is 1800, and the smallest c
- Significant 9321
Only herbs with 5 and 7 leaves grow in the Old Forest. When the boar Vavřínec collects raw materials for herbal liquor, it always tears off the whole herb and puts it in a basket. What is the most significant number of letters he will ever manage to have - Determine 8611
Determine all natural numbers A and B pairs for which the sum of twice the least common multiple and three times the greatest common divisor of natural numbers A and B is equal to their product. - Dance group
The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group? - 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. - Reminder and quotient
There are given numbers A = 135, B = 315. Find the smallest natural number R greater than one so that the proportions R:A, R:B are with the remainder 1.
- The florist
The florist had 200 roses in the morning. During the day, more than half sold it. The remaining roses will tie to the bouquet. One always remains if a bouquet of 3, 4, 5, or 6 roses is bound. How many roses from the morning shipment were sold? - Four poplars
Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be? - Trees in alley
There are four trees in the alley between which the distances are 35m, 15m, and 95m. Trees must be laid in the spaces so that the distance is equal and maximum. How many trees will they put in, and what will be the distance between them? - 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. - Exercisers
How many exercisers are in the gym (minimum number) if there is one left after ordering into three, four, and five steps?
- Dance ensemble
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? - 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? - Three friends
Three friends had balls in a ratio of 2:7:4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together. - Mathematics 6522
There are more than 20 but less than 40 students in the class. A third of the pupils wrote the mathematics test with a one, a sixth with a two, and a ninth with a three. Nobody got a four. How many students in the class wrote the test on a five? - School
Less than 500 pupils attend school. When it is sorted into pairs, one pupil remains. Similarly, one remains when sorted into 3, 4, 5, and 6 members teams. Sorted to seven members teams, no left behind. How many pupils are attending this school?
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