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)?

Result

x =  54 dm

Solution:

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

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Following knowledge from mathematics are needed to solve this word math problem:

Do you want to calculate least common multiple two or more numbers? Do you want to calculate greatest common divisor two or more numbers? Do you want to convert length units?

Next similar math problems:

1. Monkey
Monkey fell in 38 meters deep well. Every day it climbs 3 meters, at night it dropped back by 2 m. On what day it gets out from the well?
2. Rectangle
The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
3. Mistake
Nicol mistake when calculate in school. Instead of add number 20 subtract it. What is the difference between the result and the right result?
4. Line
Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
5. Diophantus
We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A.D. Thanks to an admirer of his, who described his life by means of an algebraic riddle, we know at least something about his life. Diophantus's youth l
6. Four pupils
Four pupils divided $1485 so that the second received 50% less than the first, the third 1/2 less than a fourth and fourth$ 154 less than the first. How much money had each of them?
7. Closest natural number
Find the closest natural number to 4.456 to 44.56 and to 445.6.
8. Year 2020
The four-digit number divided by 2020 gives a result of 1, **. (Can not be in form 1,*0. ) Write all the options.
9. Divisibility
Is the number 761082 exactly divisible by 9? (the result is the integer and/or remainder is zero)
10. Server
Calculate how many average minutes a year is a webserver is unavailable, the availability is 99.99%.
11. Youth track
Youth track from Hronská Dúbrava to Banská Štiavnica which announced cancellation attracted considerable media attention and public opposition, has cost 6.3 euro per capita and revenue 13 cents per capita. Calculate size of subsidies to trip group of 28.
12. Camp
In the camp are children. 1/2 went on a trip, 1/4 went to bathe and 38 children remained in the room. How many children are in camp?
13. When will I be a millionaire?
Barry monthly send 280 euros to the bank, which he deposits bear interest of 2.1% p. A. Calculate how many months must Barry save to save 1000000 euros? Inflation, interest rate changes, or bank failures ignore.
14. Diofant 2
Is equation ? solvable on the set of integers Z?
15. Diofant equation
In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
16. Class
When Pythagoras asked how many students attend the school, said: "Half of the students studying mathematics, 1/4 music, seventh silent and there are three girls at school." How many students had Pythagoras at school?
17. Gauss
Help little C.F. Gauss sum all the integers from 1 to 400.