What is the largest 4-digit number that is divisible by 10,15 and 18?
- A9900
- B9090
- C9990
- D9999
Solution & Step-by-step Explanation
Any number divisible by 10,15, and 18 must also be divisible by their Least Common Multiple (LCM).
First, find the LCM(10,15,18):
10=2×5
15=3×5
18=2×3
2
LCM=2×3
2
×5=2×9×5=90
The largest 4-digit number is 9999. We divide 9999 by 90 to find the remainder:
90
9999
=111 with a remainder of 9
To get the largest 4-digit number perfectly divisible by 90, subtract the remainder from 9999:
Largest 4-digit number=9999−9=9990
First, find the LCM(10,15,18):
10=2×5
15=3×5
18=2×3
2
LCM=2×3
2
×5=2×9×5=90
The largest 4-digit number is 9999. We divide 9999 by 90 to find the remainder:
90
9999
=111 with a remainder of 9
To get the largest 4-digit number perfectly divisible by 90, subtract the remainder from 9999:
Largest 4-digit number=9999−9=9990