Question

Find the smallest 5 – digit number exactly divisible by 6, 8 and 45​

Answer 1

Answer:

Answer is 10080

Find the LCM of the numbers for which we first factorize the numbers as follows:

rule of 45=divisible by 45 implies divisible by 5&9

In order to be divisible by 5, the last digit has to be 0 or 5, in this case 0 making no sense, as the number is palindromic and the last digit has to be same as the leftmost digit, which can't be 0.

Now, it must also be divisible by 9, implying the sum of digits must be divisible by 9.

1+0+0+8+0=9which is multiple of 9

Hence it is divisible by 45

rule of 6=it should be divisible by 2 and 3

divisabilty rule of 2=units should be 0,2,4,6,8

so it is divisible by 2.

divisabilty rule of 3=sum of digits should be multiple of 3

1+0+0+8+0=9which is multiple of 3.

so it is divisible by 3

Hence it is divisible by 6

rule of 8=units and tens should be multiple of 8

10080= 8×10=80

Hence it is divisible by 8

.°. the Answer = 10080.