Reason + least common multiple (LCM) - practice problems
Number of problems found: 72
- Eggs in basket
If the eggs in a basket are removed twice at a time, one will remain. Two eggs will remain if the eggs are removed three at a time. If the eggs are removed four, five, or six at a time, the three, four, and five eggs will remain, respectively. However, no - Condition 83228
Three boys Ivo, Vlado and Alan are reading the same book, with the condition that they will read the same number of pages every day during the entire reading until they finish the book. Ivo reads 18 pages from it every day, Vlado reads 24 pages, and Alan - 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. - Smallest z9
Find the smallest positive numbers a and b for which 7a³ = 11b⁵ - Differences 80551
Bolek and Lolek each had their own arithmetic sequence. Both Lolek and Bolek's sequence started with the number 2023 and ended with the number 3023. The two sequences had 26 numbers in common. The ratio of Bolek's and Lolka's difference was 5:2. What is t - Divisible 79464
The teacher wrote a number less than 50,000 on the board. The first student said: This number is divisible by 2 The second student said: This number is divisible by 3 And so on, down to the last one who claimed it was divisible by 13. Two in a row lied. W - Owl A,B,C
Owl a gives a hoot every 7 minutes. Owl b gives a hoot every 9 minutes. Owl c gives a hoot every 5 minutes except when he has heard owl a or b give a hoot within the previous 2.5 minutes. If this happens, owl c doesn't give a hoot. If all three owls give - 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? - Increased 64324
The number of books in the city library increased by 0.2% in 2008 and 0.6% in 2009. At the same time, the total number of books remained less than 300,000. How many books were added to the city library in 2009? - Dolls
Dorotka cut the doll's way out of two batches. She was always left with one more doll, with every two dolls cut out. How many dolls did they cut in total if the number counted 16 of them in the first cut-out? - Mr. Product
The product of ages of all of Mr. Product's children is 1408. The age of the youngest child is equal to half the age of the oldest child. How many children does Mr. Product have, and how old are they? - 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? - Lcm = 22 + gcd
The least common multiple of two numbers is 22 more than their greatest common divisor. Find these numbers. - Rectangular 54871
The arranger has at his disposal a certain number of colored targets, from which he wants to create a rectangular pattern of a flower bed. If he puts 4,5,6,8,9, or 10 targets in one row, he always has three extra targets. How many targets does it have? De - Athletics team
All athletes from the Ostrava athletics team can start in four, five, six, and seven stages, and no one will be present. How many average athletes are in one athletic group if there are twelve groups in the section? Consider the smallest number of athlete - Coloured numbers
Mussel wrote four different natural numbers with colored markers: red, blue, green, and yellow. When the red number divides by blue, it gets the green number as an incomplete proportion, and yellow represents the remainder after this division. When it div - 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, one rose will always be left. Det - School year
At the beginning of the school year, 396 notebooks and 252 textbooks were 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 t - Intelligence test
Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus seven 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 tes - 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 and their products was the power of the prime number. Find all possible ticket prices.
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