find the least 5-digit number which on dividing by 4,12,20 and 24 leaves remainder 3 in each case

We have to find a 5 digit number which on dividing by 4,12,20 and 24 leaves remainder 3 in each case.

So,

LCM(4,12,20,24) = 120

So to obtain a five digit number we have to multiply the LCM by 84.

Therefore the required number

= 10080 + 3

= 10083

**
**