Least number which when divided by 5,6,7,8 and leaves
remainder 3. but when divided by 9 leaves no demainder.
Answers
Answered by
1
Answer:
there is not any number of such type.
Answered by
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.
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