The least number that should be added to 2397 so that the sum is exactly divisible by 3,4,5 and 6?
- A6
- B4
- C5
- D3
Solution & Step-by-step Explanation
First, find the LCM of 3,4,5, and 6:
3=3
4=2
2
5=5
6=2×3
LCM(3,4,5,6)=2
2
×3×5=4×3×5=60
Now, divide 2397 by 60 to find the remainder:
60
2397
=39 with a remainder of 57
Since 60×39=2340 and 2397−2340=57.
The next multiple of 60 after 2397 is:
60×40=2400
The least number to be added is:
Number to be added=2400−2397=3
Alternatively: LCM−Remainder=60−57=3
3=3
4=2
2
5=5
6=2×3
LCM(3,4,5,6)=2
2
×3×5=4×3×5=60
Now, divide 2397 by 60 to find the remainder:
60
2397
=39 with a remainder of 57
Since 60×39=2340 and 2397−2340=57.
The next multiple of 60 after 2397 is:
60×40=2400
The least number to be added is:
Number to be added=2400−2397=3
Alternatively: LCM−Remainder=60−57=3