What is the least number which when divided by 7,8,11 always gives 6 as the remainder
Answers
Answer:
622
Step-by-step explanation:
LCM
7×8×11=616
remainder is 6
then
161+6=622
Given:
Three numbers 7, 8, 11.
To Find:
The least number such that it leaves a remainder 6 when it is divided by 7, 8, and 11.
Solution:
The given problem can be solved using the concepts of LCM.
1. The given numbers are 7, 8, and 11.
2. The LCM is defined as the least common multiple of all the three numbers such that the remainder is zero when it is divided by any of the given numbers.
3. The LCM of 7, 8, and 11 is,
=> LCM of 7 and 8 is 56 as they are relatively prime.
=> LCM of 56 and 11 is 616.
4. Since the LCM of 7, 8, and 11 is 616. The number 616 is divisible by all the three numbers 7, 8, and 11. Hence,
=> 616 + 1 leaves a remainder of 1 when divided by 7, 8, and 11.
=> 616 + 2 leaves a remainder of 2 when divided by 7, 8, and 11.
=> 616 + 3 leaves a remainder of 3 when divided by 7, 8, and 11.
=> 616 + 6 leaves a remainder of 6 when divided by 7, 8, and 11.
=> 616 + 6 = 622.
Therefore, the least number is 622.