What is the greatest 3-digit number divisible by 4, 5 and 6?
- A990
- B930
- C960
- D900
Solution & Step-by-step Explanation
To find the numbers divisible by 4, 5, and 6, we first find their Least Common Multiple (LCM).
LCM(4,5,6)=60
Any number divisible by 4, 5, and 6 must be a multiple of 60.
The greatest 3-digit number is 999.
Divide 999 by 60 to find the closest multiple:
999÷60=16 remainder 39
Subtract the remainder from 999 to get the largest perfectly divisible multiple:
999−39=960
Alternatively:
60×16=960
Thus, 960 is the greatest 3-digit number divisible by 4, 5, and 6.
LCM(4,5,6)=60
Any number divisible by 4, 5, and 6 must be a multiple of 60.
The greatest 3-digit number is 999.
Divide 999 by 60 to find the closest multiple:
999÷60=16 remainder 39
Subtract the remainder from 999 to get the largest perfectly divisible multiple:
999−39=960
Alternatively:
60×16=960
Thus, 960 is the greatest 3-digit number divisible by 4, 5, and 6.