Q1.
Find the least number which is exactly divisible by 12, 15, and 18.
Q2.
Find the greatest number that will exactly divide 96 and 404.
Q3.
Three bells ring at intervals of 20, 25, and 30 minutes. If they all ring together at 6:00 AM, when will they next ring together?
Q4.
Find the greatest number that will divide 289 and 397 leaving remainders 5 and 7 respectively.
Q5.
The product of two numbers is 960 and their HCF is 8. Find their LCM.
Q6.
Find the smallest number which when divided by 15, 20, and 25 leaves a remainder of 5 in each case.
Q7.
Find the greatest number that divides 184, 248, and 304 exactly.
Q8.
Find the LCM of 9, 12, and 15.
Q9.
The HCF of two numbers is 18 and their LCM is 360. If one number is 90, find the other.
Q10.
Find the least number which when divided by 16, 24, and 36 leaves a remainder of 4 in each case.
Q11.
Three pieces of rope measure 240 cm, 360 cm, and 600 cm. What is the greatest length of rope that can be cut from each without any leftover?
Q12.
Find the least number that is exactly divisible by 6, 9, 15, and 18.
Q13.
Two cyclists start together and take 20 minutes and 30 minutes respectively to complete one round of a circular track. After how much time will they meet again at the starting point?
Q14.
Find the HCF and LCM of 24 and 36.
Q15.
Find the least number which when divided by 35, 45, and 55 leaves the same remainder of 5 in each case.
Q16.
Find the least number which leaves the same remainder when divided by 20, 28, and 36 and the remainder is less than all divisors.
Q17.
A gardener has 360 marigold plants, 432 rose plants, and 504 tulip plants. He wants to plant them in rows with the same number of plants and with only one type of plant per row. What is the maximum number of plants per row?
Q18.
Find the smallest 4-digit number which is exactly divisible by 12, 18, 24, and 32.
Q19.
Three tankers contain 403 litres, 434 litres and 465 litres of oil. What is the greatest capacity of a container that can measure all the quantities exactly?
Q20.
Find the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case, but is divisible by 9.
Q21.
Three traffic lights blink at intervals of 24, 36, and 48 seconds. If they blink together at 10:00 AM, at what time will they blink together again?
Q22.
Find the greatest number which divides 1251, 9377 and 15628 leaving the same remainder in each case.
Q23.
A group of students is arranged in rows of 12, 18, and 27. In each case, 9 students are left out. What is the least number of students in the group?
Q24.
Find the smallest number which when divided by 35, 45, and 55 gives remainder 18 in each case.
Q25.
Find the largest number which exactly divides 765, 867, and 918.
Q26.
Find the least number which is a perfect square and exactly divisible by 6, 12, and 18.
Q27.
Find the greatest number which divides 1224, 1312, and 1536 leaving remainders 6, 14, and 38 respectively.
Q28.
The LCM of two numbers is 2520 and their HCF is 10. If one number is 140, find the other.
Q29.
A man has 252 apples, 198 oranges, and 144 mangoes. He wants to pack them into identical boxes so that each box contains only one type of fruit and the number of fruits in each box is the maximum possible. How many total boxes does he need?
Q30.
Find the least number which is divisible by 15, 20, 24 and is a perfect cube.