Least common multiple (LCM) - practice for 14 year olds - page 2 of 3
Number of problems found: 43
- 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. - 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. - Two gears
The gearbox will use a large gear to turn a smaller gear. The large gear will make 75 revolutions per minute, while the smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM
- 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? - Two buses
The first bus runs for 15 minutes. The second bus runs after 21 minutes. Together they both leave at 7:00 on Monday. When and what day will they meet? - 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? - Newspapers 5601
Four deliver newspapers. One takes 60 minutes, the second 40 minutes, the third 120 minutes, and the fourth 80 minutes. If they left at the same time, at 8 o'clock, when will they meet again at the place they left? - Different 5402
Adélka had two numbers written on the paper. When she added their greatest common divisor and least common multiple, she was given four different numbers less than 100. She was amazed that if she divided the largest of these four numbers by the least, she
- Minutes 5310
They had three tower clocks in the city. Some went right, the others were 10 minutes ahead of the day, and the thirds were 12 minutes late each day. One day they struck all the clocks at noon at once. How long will it be like this again? - Pardubická 4651
Jirka decided to divide the winnings from the bet in Velká Pardubická between himself and his three younger brothers according to age in the ratio of 2:3:5:7. They paid each amount in whole crowns. One of the amounts was CZK 679. How big was the win? - Pyramid Z8–I–6
Each brick of the pyramid contains one number. Whenever possible, the number in each brick is the lowest common multiple of two numbers of bricks lying directly above it. May that number be in the lowest brick? Determine all possibilities. - One-sixth 3279
If I had half as many nuts as I have now, I would have the same as Vendulka. If Vendulka had a third less than she has now, she would have the same size as me. If she had one-sixth less than she has and gave me that part, we would have the same amount. Ho - Four classses
Students of all 7, 8, and 9 classes in one school may take up 4,5,6, and 7 abreast, and nobody will be left. How many is the average count of pupils in one class if there are always four classes in each grade?
- Ski tow
The ski club has 168 pupils and uses a lift with 60 seats, while students always follow the same sequence in filling seats. How often while riding a ski lift has the skier sitting in the same seat as the first run? - 9.A
Class 9A attends more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, and the ninth to mark 3. No one gets mark 4. How many students of class 9A wrote a test to mark 5? - Two months
Mars has two months, Phobos and Deimos. Phobos orbit around Mars in 7 hours 39 minutes, and Deimos in 30 hours 14 minutes. How long will the relative positions of the three celestial bodies repeat? - Parachutists
During freefall, parachutists were first held in groups of 4, then 6, then 9, 12, and finally 18 members. How many parachutists jump at least should be, if at each group must all be involved. - Seamstress 2
Seamstress bought two kinds of textile in whole meters. One at 50 SKK and the second 70 SKK per meter. How many meters were bought from these two textiles when paid 1540 SKK totally?
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