# Least common multiple (LCM) - math word problems

#### Number of problems found: 104

• Two gears
Two gears with 13 and 7 teeth rotate locked into each other. How many turns does a big wheel have to make for both wheels to be in the starting position again?
• Three ships
There are three ships moored in the port, which sail together. The first ship returns after two weeks, the second after four weeks, and the third after eight weeks. In how many weeks the ships will meet in the port for the first time? How many times have
• Drivers
Driver Franta and driver Karel are friends. They leave the start-stop both at the same time in the afternoon - at 13.30. When will they meet again if Franta goes around his route in 50 minutes and Karel in 40 minutes?
• School year
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
• Lamps on playground
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?
• Ratio
Alena collected 7.8 kg of blueberries, 2.6 kg of blackberries, and 3.9 kg of cranberries. Express the ratio in the smallest natural numbers in this order.
• Tram stop
The blue tram stops every 12 minutes, the red one 8 minutes. At 8 o'clock they left the stop together. How many times do they meet at a stop before 11 am?
• The florist
A consignment of 200 roses arrived at the florist in the morning. She sold more than half of them during the day. She wants to tie bouquets of the remaining roses. If she ties a bouquet of three, four, five or six roses, there will always be one rose left
• 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?
• Length of a string
What is the smallest length of a string that we can cut into 18 equal parts and even 27 equal parts (in decimeters)?
• Intelligence 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
• 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?
• The smallest number
What is the smallest number that can be divided by both 5 and 7
• 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?
• What is 3
What is the least common denominator of 11/15 and 12/19?
• A large
A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. 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. ]
• LCM of two number
Find the smallest multiple of 63 and 147
• Two buses
The first bus runs 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?
• Counting number
What is the smallest counting number divisible by 2,5,7,8 and 15?
• 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 the same and the maximum. How many trees will they put in and what will be the distance between them?

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