Search problems

5 problems match “least common multiple”. Clear

Least integer with consistent remainders ●●○○○ 20 ptsWhat is the least positive integer which when divided by 5 gives a remainder of 4, when divided by 6 gives a remainder of 5, when divided by 7 gives a remainder of 6, when divided by 8 gives a remainder of 7, when divided by 9 gives a remainder of 8, and when divided by 10 gives a remainder of 9?
Smallest multiple beyond 2010 with terminating decimals ●●○○○ 20 ptsLet $S$ be the set of all integers $k$ such that $\frac{17k}{66}$ and $\frac{13k}{105}$ are both terminating decimals. What is the smallest integer in $S$ that is greater than 2010?
Maximum elephants with a unique distribution ●●●○○ 50 ptsOstap Bender organized an elephant giveaway in the city of Fux. 28 union members and 37 non-members showed up, and Ostap distributed the elephants so that all union members received the same number of elephants and all non-members received the same number of elephants (the two numbers may differ). It turned out that there was only one way to distribute the elephants so that all of them were given away. What is the maximum number of elephants Ostap Bender could have had? (Each person who came received at least one elephant.)
Exactly two friends visiting Daphne ●●●○○ 50 ptsDaphne is visited periodically by her three best friends, Alice, Beatrix and Claire. Alice visits every third day, Beatrix every fourth day, and Claire every fifth day. All three friends visited Daphne yesterday. On how many days of the next 365-day period will exactly two friends visit her?
Least integer with percentage conditions ●●●○○ 50 ptsLet $N$ be the least positive integer that is both 22 percent less than one integer and 16 percent greater than another integer. Find the remainder when $N$ is divided by 1000.