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