Question

Find the least 5 digit number which leaves remainder 3 in each case when divided by 5 10 12 15 18 25 and 30

Answer 1

Here we have to find the LCM of 5, 10,12,15,18,25 and 30. because the LCM of 10,12,15,18,25 and 30 will be completely divisible be 10,12,15,18,25 and 30.

So, to find LCM we have to write prime factorisation of each number
10 = 2x5
12 = 2x2x3
15 = 3x5
18 = 2x3x3
25= 5x5
30= 2x3x5

So, LCM of 10,12,15,18,25 and 30 will be
= 2x2x3x3x5x5
= 900

that mean if we add 3 in multiple of 900 and then divide by any of the number among 10,12,15,18,25 and 30 it will always leave a remainder of 3.

least 5 digit multiple of 900
= 900x100
=90000

So the required number is
= 90000+3
=90003