Find the Number
Lowest number which leaves 3 as remainder when divided by 6, 8, or 10
Answers
search-icon-header
Search for questions & chapters
search-icon-image
Question
Bookmark
The least number which when divided by 5,6.7 or 8 leaves the remainder 3 in each case, but when divided by 9 leaves no remainder, is
Medium
Solution
verified
Verified by Toppr
Correct option is B)
Let the number be x.
When x is divided by 5, 6, 7 or 8, it leaves remainder 3.
∴x must be in the form of (k×y+3),
where, k is a constant ⇒k=1,2,3...
y is the Least Common multiple (LCM) of 5, 6, 7 and 8
∴y=LCM(5,6,7,8)
⇒y=LCM(LCM(5,6),LCM(7,8))
⇒y=LCM(30,56)
⇒y=840
∴x=840×k+3
For different values of k, we get different values of x.
k=1⇒x=843, is indivisible by 9
k=2⇒x=1683, is divisible by 9
∴1683 is the number
which when divided by 5, 6, 7 or 8 leaves the remainder 3 in each case,
but when divided by 9 leaves no remainder.