Question

Find the greatest number of 5 digits which when divided by 45, 60 and 75 leaies 20 as remainder in each case.​

Answer 1

ANSWER

The LCM of 3,12,18,24,30,36 is 360

We have the greatest five digit number : 99999

When 99999 is divided by 360, leaves the remainder 279

So, 99999−279=99720

Now here, we can see that

3−2=1, 12−11=1, 18−17=1, 24−23=1, 30−29=1, 36−35=1

The difference of divisors and their corresponding remainders is 1.

So, the required five digit number will be 1 less than $99720$$.

The required number is 99720−1=99719

Answer 2

Answer:

take l.c.m and divide 99999