Least common multiple (LCM) + greatest common divisor (GCD) - math problems

Number of problems found: 24

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)
LCD 2
The least common denominator of 2/5, 1/2, and 3/4
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)?
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.
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.
Square tiles
The room has dimensions of 12 meters and 5.6 meters. Determine the number of square tiles and their largest dimension to exactly cover the floor.
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?
Cubes
Carol with cut bar 12 cm x 12 cm x 135 cm to the cubes. Find the sum of all the surfaces of the resulting cubes.
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?
The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
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?
Apples and pears
Mom divided 24 apples and 15 pears to children. Each child received the same number of apples and pears - same number as his siblings. How many apples (j=?) and pears (h=?) received each child?
Plumber
The plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it?
Three friends
Three friends had balls in ratio 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.
Garden
The garden has the shape of a rectangle measuring 19m20cm and 21m60cm. Mr. Novák will fence it. It wants the distance between adjacent pillars to be at least two meters and a maximum of three meters. He would also like the distances between the adjacent p
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?
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. ]
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?
Around the flowerbed
Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses found in every corner of the flowerbed and consumed them as little as possible. a) At what distance are planted roses? b) How many ros