Find the greatest 3 digit number which when divided by 75,45 and 60 leaves no remainder and the remainder 4 in each case

LCM of 75,45 and 60 is 900.
The divisor of 75,45 and 60 must be a multiple of their LCM.
75×900=67500 )⤵
45×900=40500 )↪ not a 3 digits no.
60×900=54000 )⤴
Since they are not 3 digits no..the greatest 3 digits no exactly divisible by 75,45,60 must be the LCM itself i.e. 900 >>Ans

Now,the next question is very simple.As the 900
greatest divisor of all given no., add 4 to get remainder 4 when divided by 75,60 and 45.
So, ans=904