Question

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

Answer 1

Least 5 digit number  = 10000

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

Dividing 10000 by 120 leaves a remainder 40 , Subtract 40 from 10000 = 9960

So this means 9960 is divisible by 120

9960 + 120 = 10080

To find the number which leaves remainder 3, we have to add 3 to 10080

10080 + 3 = 10083

Hope this helps...

Answer 2

Least 5 digit number is 10000

Step 1 : Find the LCM of 4, 12, 20 and 24

4 = 2 × 2

12 = 2 × 2 × 3

20 = 2 × 2 × 5

24 = 2 × 2 × 3 × 2

LCM = 120


Step 2 : Divide 10000 by 120

After dividing we get remainder as 40


Step 3 : Subtract 40 from 10000

10000 - 40 = 9960


This means that 9960 is divisible by 120


Step 4 : Add 120 to 9960

9960 + 120 = 10080


Step 5 : Add 3 to 10080

10080 + 3 = 10083


∴ The number is $\large{\boxed{\boxed{\rm{10083}}}}$