Question

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

Answer 1

As per data,

We have to find the least five digit number which gives remainder 3 when divided by each of the numbers - 5, 10, 12, 18, 30, 25

For finding the required number,

We will first find the LCM of the given number.

So, LCM of 5, 10, 12, 18, 30, 25 will be,

$5 = 5\times 1\\10 = 5\times 2\\12 = 3 \times 2 \times 2\\18 = 3\times 3 \times 3 \times 2\\25 = 5 \times 5\\30 = 5\times 2 \times 3\\=> LCM = 5\times 2 \times 3 \times 2 \times 3 \times 3 \time 5 \\=> LCM = 450$

As the number should gives remainder 3 in each case.

So, least number will be = 450 +3 = 453

As, 453 is not a five digit number,

So, the general equation of such five digit number will be

$450 n +3\\where\: n = 1,2,3$

Hence, such required number will be,

$=(450 \times 23) +3 \\=> 10350+3\\=> 10353$