Question

The greatest number of five digits which when divided by 3,5,8,12 leave 2 as remainder is

Answer 1

First we find out the greatest 5 digit number, which when divided by 10, 13 , 15 & 26 gives remainder 0

=> That greatest number will be divisible by the LCM of 10, 13,15 & 26

Hence,LCM =

10 = 2 x 5

13 = 13 x 1

15 = 3 x 5

26 = 2 x 13

=> lcm = 2 x 3 x 5 x 13 = 390

Now, greatest 5 digit number divisible by 390 =

99999 ÷ 390 = quotient = 256, remainder = 159

So, 99999 - 159 = 99840

99840 is the greatest 5 digit number divisible by 10, 13, 15, 26 . But we need remainders 4,7,9,20.

& since 10–4 =6, 13–7 = 6, 15–9 = 6 26 -6 = 20

99840 - 6 = 10 x 9984 +4

99840 -6 = 13 x 7680 + 7

99840 -6 = 15 x 6656 + 9

99840 -6 = 26 x 3840 +20

Hence the required 5 digit number

= 99840 - 6

= 99834 …………..ANS

Answer 2

Answer:

The greatest number of five digits which when divided by 3,5,8,12 leave 2 as remainder is 99834.