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)?

Correct answer:

x =  54 dm

Step-by-step explanation:

$$\begin{gathered} 18=2\cdot 3^2 \\ 27=3^3 \\ LCM(18,27)=2\cdot 3^3=54 \\ x=LCM(18,27)=54\text{ dm} \end{gathered}$$

Try another example

Related math problems and questions:

• Decompose
  Decompose into primes and find the smallest common multiple n of (16,20) and the largest common divisor D of the pair of numbers (140,100)
• A rope
  A rope can be cut into equal length with no rope left over. The lengths can be 15cm,18cm or 25cm. What is the shortest possible length of the rope?
• Paving - joints
  We are paving with rectangular pavement 18 cm × 24 cm was placed side by side in height in a row and in the second row in width etc. How many times will the joints meet at a distance 10 m?
• 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.
• LCD 2
  The least common denominator of 2/5, 1/2, and 3/4
• LCM of two number
  Find the smallest multiple of 63 and 147
• School books
  At the beginning of the school year, the teacher distributed 480 workbooks and 220 textbooks. How many pupils could have the most in the classroom?
• The classroom
  The classroom is 9 meters long. The width of the classroom is smaller and can be passed in equally long steps of 55 CM or 70 CM. Determine the width of the classroom.
• Glass panel
  A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?
• Blades
  1st blade 2,5 m, 2nd blade. .1.75 m. How many same long pieces of this two blades can be do the biggest? How long is one piece?
• 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?
• Segments
  Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
• LCM
  What is the least common multiple of 5, 50, 14?
• Lcm of three numbers
  What is the Lcm of 120 15 and 5
• The smallest number
  What is the smallest number that can be divided by both 5 and 7
• Identical cubes
  From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12dm x 16dm x 20dm?
• Tractor wheels
  The front wheel of the tractor has a circumference of 18 dm and the rear 60 dm. We will make a red mark on the lowest point of both wheels. The tractor then starts. At what distance from the start will both marks appear identically at the bottom again?