The least number, which when divided by 5, 6, 7, and 8 leaves a remainder 3 in each case, but when divided by 9 leaves no remainder, is:
1683
The least number divisible by 5, 6, 7, and 8 is their LCM, which is 840. Then, adding 3 to the result gives 843. Now, check for divisibility by 9: 843 is divisible by 9. The correct number is 1683.
Similar Questions
The product of two 2-digit numbers is 2160 and their H.C.F. is 12. The numbers are
The LCM of 2³ x 9² x 13, 2² x 13² x 19 and 9³ x 13² x 19² is:
A and B start running at the same time and from the same point around a circle. If A can complete one round in 40 seconds and B in 50 seconds, how many seconds will they take to reach the starting point simultaneously?
Arvind and Chetan started running simultaneously from the same point in the same direction on a circular track of length 210 m. If Arvind takes 180 seconds to complete one round, and Chetan takes 420 seconds to complete one round, after how much time will they meet for the first time at the starting point on the track?
Find the LCM of 12, 18, 30.
- Find the smallest number which when divided by 8, 9, and 12 leaves a remainder of 5 in each case.
- The product of two numbers is 2025, and their HCF is 15. What is their LCM?
- What is the least square number that is divisible by 8, 12, and 20?
Important Questions from LCM and HCF
The HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
