Reason + least common multiple (LCM) - practice problems
Number of problems found: 72
- Lcm = 22 + gcd
The least common multiple of two numbers is 22 more than their greatest common divisor. Find these numbers. - Unknown integer
Find the smallest integer: Divided by 2, the remainder is 1. divided by 3. The remainder is 2. divided by 4. The remainder is 3. Divided by eight, the remainder is 7. Divided by 9, the remainder is 8. - Smallest z9
Find the smallest positive numbers a and b for which 7a³ = 11b⁵ - 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? - 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. - Exercisers
How many exercisers are in the gym (minimum number) if there is one left after ordering into three, four, and five steps? - 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? - 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. - What is 20
What is the least number that should be added to 2497 so that the sum of the digits is divisible by 5, 6, and 10? - Class 9A
On the final certificate, one-quarter of the class 9A marked “C” in mathematics, the seventh mark “C” from the Czech language, and two students failed in chemistry. How many students attend class 9A? - Regularly 7749
Three steamers leave the port. The first regularly returns after three months, the second after four, and the third after six months. How long before they meet again in the port? - Participate 5543
The dance group is preparing for a performance. The program includes dances in pairs, fours, and fives. How many members does a group have to have to dance all these dances and have all their members participate in each dance? - Dividing
One always remained when dividing the tangerines into packages of 8 or 10. How many were there, if more than 250 and less than 300? - 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. - Tiles
How many tiles of 20 cm and 30 cm can build a square if we have a maximum of 100 tiles? - Fewer than 500 sheep,
There are fewer than 500 sheep, but if they stand in a double, triple, quadruple, five, and sixth-order, one sheep will remain. But they can stand in the seventh order. How many sheep? - Mathematics 2980
More than 20, but less than 40 pupils go to 1.S. A third of the pupils wrote the mathematics test with a one, a sixth with a two, and a ninth with a three. No one got a high five. How many 1.S pupils wrote the test with a four? - Neither 4182
Hanka gave Simon a riddle: guess a pair of numbers whose GCD is 7, and LCM is 90. Katy wanted Šimon to guess such a pair for which GCD is 7, and LCM is 91. Which riddle could Šimon guess? A: Katy B: Hankina C: neither D: Both - Determine 82852
The fan club has 275 members. Some members went to the match by train. Determine how many members rode when they could fill the wagons with either 60 or 80 seats. - 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.
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