Question

Least number which when divided by 5,6,7,8 and leaves
remainder 3. but when divided by 9 leaves no demainder.​

Answer 1

Answer:

there is not any number of such type.

Answer 2

Answer:

Least number which when divided by 5,6,7 and 8 leaving remainder 3 =

LCM of 5,6,7 and 8.

(i) Prime factorization of 5 = 5

(ii) Prime factorization of 6 = 2 * 3

(iii) Prime factorization of 7 = 7

(iv) Prime factorization of 8 = 2 * 2 * 2

LCM(5,6,7,8) = 5 * 3 * 2 * 2 * 2 * 7

                     = 840.

Given that it leaves a remainder 3.

So, the number is of the form = 840k + 3{bq + r}

When k = 1:

= > 840(1) + 3

= > 843

Not divisible by 9 and leaves remainder 6.

When k = 2:

= > 840(2) + 3

= > 1680 + 3

= > 1683.

Divisible by 9 and leaves no remainder.

Therefore, the least number is 1683.