Practice HCF & LCM Practice Questions with Detailed Solutions – Level 3

What is the least number that leaves a remainder of 5 when divided by 12, 18, 21 or 28, but is exactly divisible by 13?

What is the smallest five-digit number which, when divided by 15, 20 and 24, leaves remainders 8, 13 and 17 respectively?

The greatest number that divides 1399, 2272 and 3824 leaving the same remainder in each case is N, and that common remainder is R. What are N and R respectively?

Four temple bells toll at intervals of 1.2 minutes, 1.8 minutes, 2.4 minutes and 3 minutes respectively. They first toll together at 7:00 a.m. How many times will they toll together from 7:00 a.m. to 1:00 p.m., counting both these times?

By what number must the HCF of \( \frac{2}{3} \), \( \frac{8}{9} \), \( \frac{16}{81} \) and \( \frac{10}{27} \) be multiplied to get their LCM?

Three ropes are 2.7 m, 4.5 m and 6.3 m long. All of them are to be cut into pieces of equal length, with no rope left over. What is the least possible total number of pieces?

The HCF of two numbers is 16 and their product is 7680. How many such pairs of numbers are possible?

The sum of two numbers is 420 and their HCF is 15. How many such pairs of numbers exist?

Rohit, Sameer and Imran start running together from the same point on a circular track at 10:00:00 a.m. They take 252 seconds, 308 seconds and 198 seconds respectively to complete one round. At what time will all three first be together again at the starting point?

Three cyclists start together from the same point on a 1200 m circular track and ride in the same direction at 3 m/s, 7 m/s and 11 m/s. After how many minutes will all three first be together anywhere on the track?