1.What is the smallest perfect square that is divisible by 10, 12, 15, and 18?
2.Three men begin simultaneously to run along a circular track that measures 11 kilometers in circumference. Their speeds are 4 km/h, 5 km/h, and 8 km/h respectively. After how many hours will they all meet again at the starting point together?
3.What is the smallest number that leaves remainders of 1, 2, 3, 4, and 5 when divided by 6, 7, 8, 9, and 10 respectively, and is also exactly divisible by 19?
4.What is the smallest multiple of 13 that, when divided by 6, 8, and 12, leaves remainders of 5, 7, and 11 respectively?
5.What is the smallest number that leaves remainders of 1, 2, 3, 4, and 5 when divided by 2, 3, 4, 5, and 6 respectively, and is exactly divisible by 7?
6.A pile of stones can be evenly divided into groups of 21 without any remainder. However, when the stones are grouped into sets of 16, 20, 25, or 45, there are always 3 stones left over. What is the smallest possible number of stones in the pile?
7.What is the largest four-digit number that leaves remainders of 4, 9, 15, and 22 when divided by 10, 15, 21, and 28 respectively?
8.What is the smallest number that leaves a remainder of 25 when divided by 35, a remainder of 15 when divided by 25, and a remainder of 5 when divided by 15?
9.Find the smallest number that, when divided by 8, 12, 18, and 24, leaves remainders of 4, 8, 14, and 20 respectively.
10.Three wheels rotate around the same horizontal axis, completing 15, 20, and 48 revolutions per minute respectively. If they all start from the same point on their circumference facing downward, after how much time will they align again at that exact position?
11.Two numbers, 4242 and 2903, when divided by the same three-digit divisor, leave identical remainders. What is the divisor?
12.Four prime numbers are arranged in increasing order. The product of the first three primes is 385, while the product of the last three primes is 1001. What is the value of the fourth prime number?
13.Four prime numbers are arranged in increasing order. The product of the first three primes is 7429, while the product of the last three primes is 12673. What is the value of the fourth prime number?
14.What is the minimum number of square slabs, each with whole number side lengths, needed to cover a floor measuring 12.96 meters in length and 3.84 meters in width?
15.A rectangular room measures 4 meters 37 centimeters in length and 3 meters 23 centimeters in width. If the floor is to be covered completely with square tiles of the largest possible size without cutting, how many such tiles will be needed?
16.Determine the maximum side length of square tiles that can be used to cover the floor of a room measuring 5 meters 44 centimeters in length and 3 meters 74 centimeters in width without any gaps or overlaps.
17.A tea wholesaler has 408 kg, 468 kg, and 516 kg of three different types of tea. He wants to pack each type separately into boxes of the same maximum capacity. What is the greatest possible size of each box?
18.A trader has three quantities of milk: 435 liters, 493 liters, and 551 liters. What is the minimum number of identical-sized containers needed to store all the milk separately without mixing?
19.What is the largest number that, when dividing 697, 909, and 1227, leaves the same remainder in each case?
20.What is the largest number that divides 25, 73, and 97 leaving the identical remainder in each case?