Let us find the LCM of the given numbers 25,30 ,40
Lcm= 600
The difference in numbers from the remainder are
25-20=5
30-25=5
40-35=5
The remainder in each case is 5 less than the divisor
The greatest 5 digit number divisible by 5 is 99995
Dividing this by LCM 600
[tex] \frac{99995}{600} =166.66 [/tex] =167(rounded)
Let n+5 leaves remainder 5 when divided by 25,30,40
n+5=167 times 600
n+5=99600
n=99595
The 5 digit greatest number divided by 25,30and 40 leaving a remainder of 20, 25 and 35 respectively is 99595.
