Question

Find the largest 5 digit number divisible by 18,24 and 32

Answer 1

solution:

      By finding LCM of the 3 numbers, and applying euclid's division lemma with the smallest 6 digit number,then,subtracting the remainder,we can find rh largest 5 digit number divisible by all the 3 numbers.

                                2 I 18, 24, 32
                                   L________
                                3 I   9, 12, 16
                                   L________
                                3 I   3,  4,  16
                                   L________
                                2 I   1,  4,  16
                                   L________
                                2 I   1 ,  2,   8
                                   L________
                                2 I   1 ,  1,   4
                                   L________
                               2  I   1,   1,   2
                                   L________
                                   I   1,   1,   1

              LCM= 2^{5} x 3^{2}=32x9=288

By using EUCLID DIVISION LEMMA,
We get,
                                          a=bq+r
                              100,000=288(347)+64
                              100,000 - 64 = 99,936
 
∴The largest 5-digit number that is divisible by 18,24 and 32 is 99,936

                    HOPE IT HELPS..!