The largest number of four digits that is divisible by 12, 15 and 18 is ________.

To find the largest 4-digit number divisible by 12, 15, and 18, we first need to find the Least Common Multiple (LCM) of these numbers.
Step 1: Find the LCM of 12, 15, and 18

Prime factorization of 12=2
2
×3

Prime factorization of 15=3×5

Prime factorization of 18=2×3
2


LCM(12,15,18)=2
2
×3
2
×5=4×9×5=180
Step 2: Divide the largest 4-digit number by the LCM
The largest 4-digit number is 9999.

180
9999
​
=55 with a remainder of 99
Step 3: Subtract the remainder from 9999

Required Number=9999−99=9900
Therefore, 9900 is the largest 4-digit number divisible by 12, 15, and 18.