CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

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

A
1677
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1683
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
1697
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1703
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 1683
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=1x=843, is indivisible by 9
k=2x=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.

1112245_809570_ans_4cd2841856e24fa2bfa5b27a7c7fe972.gif

flag
Suggest Corrections
thumbs-up
1
mid-banner-image
mid-banner-image
similar_icon
Related Videos
thumbnail
lock
Division by Zero_Tackle
MATHEMATICS
Watch in App